Which of the following is not a sum of two consecutive perfect square

what perfect square number should be substracted from x so that resultant is perfect square number if solution doest not exist just tell not possible? note here x is also perfect square number example x=25 25-9= 16(perfect square number) here ans=9 x=100 100-36= 64(perfect square number) here ans=36 x=100 100-64= 36 whis perfect square number here ans=64 when x=4 ,6,3 and so on then no such answer will be exist It's a bit unclear what you're asking about, but here are a few related tidbits. You should read about $$a^2 + b^2 = c^2$$ In this case $c^2$ is your $x$ and either $b^2$ or $a^2$ are possible values for what you subtract from your $x$. You may also be interested in Given any integer, you can tell whether it can be written as the sum of two squares if you find its If all of the primes that are one less than multiples of four have even exponents in the prime factorization of your number, then it can be written as the sum of two squares. Otherwise, it cannot. You should first read Fermat's theorem on writing primes as sums of two squares if you want to understand this more general result. This is related to your original question because if $x$ can be written as the sum of two squares, then you know at least two possibilities for "perfect squares that can be subtracted from $x$ to get another perfect square" ...

(i) 121 ∵ 121 - 1 = 120 85-13 = 72 120 - 3 = 117 72 - 15 = 57 117 - 5 = 112 54 - 17 = 40 112 - 7 = 105 40 - 19 = 21 105 - 9 = 96 21 - 21 = 0 96 - 11 = 85 i.e. 121 = 1+3+5+7+9+11+13+15+17+19+21. Thus , 121 is a perfact square. (ii) 55 ∵ 55 - 1 = 54 30 - 11 = 19 54 - 3 = 51 19 - 13 = 6 51 - 5 = 46 6 - 15 = -9 46 - 7 = 39 39 - 9 = 30 Since, 55 cannot be expressed as the sum of successive old numbers starting from 1. ∴ 55 is not a perfact square. (iii) 81 Since, 81 - 1 = 80 56 - 11 = 45 80 - 3 = 77 45 - 13 = 32 77 - 5 = 72 32 - 15 = 17 72 - 7 = 65 17 - 17 = 0 65 - 9 =56 ∴ 81 = 1+3+5+7+9+11+13+15+17 Thus, 81 is a perfact square. (iv) 49 Since, 49 - 1 = 48 48 - 3 = 45 45 - 5 = 40 40 - 7 = 33 33 - 9 = 24 24 - 11 = 13 13 - 13 = 0 ∴ 49 = 1+3+5+7+9+11+13 Thus, 69 is not a perfact square. (v) 69 Since, 69 - 1 = 68 44 - 11 = 33 68 - 3 = 65 33 - 13 = 20 65 - 5 = 60 20 - 15 = 5 60 - 7 = 53 5 - 17 = 12 53 - 9 = 44 ∴ 69 cannot be expressed as the sum of consecutive odd num numbers starting fron 1. Thus, 69 is not a perfect square.

Sum of Perfect Squares Formula Before knowing what is the sum of the perfect squares formula, first, let us recall what are perfect squares. A perfect square is a number that can be written as the square of a number. 1, 4, 9, 16, 25, 36, etc are some perfect squares as they can be expressed as 1 2, 2 2, 3 2, 4 2, 5 2, 6 2, etc respectively. The sum of perfect squares formula is used to find the sum of two or more perfect squares without adding them manually. What Is the Sum of Perfect Squares Formula? We have two types of formulas for finding the sum of • The formula for finding thesum of two perfect squares is derived from one of the 2= a 2+ 2ab + b 2, which is: a 2+ b 2= (a + b) 2- 2ab • The formula for finding the sum of the squares for first "n" 1 2+ 2 2+ 3 2+ ... + n 2= [ n (n + 1) (2n + 1) ] / 6 Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps. Let us see the applications of the sum of perfect squares formulas in the following section. Examples UsingSum of Perfect Squares Formula Example 1:Find the sum of squares of 101 and 99. Solution: To find: The sum of squares of 101 and 99. i.e., 101 2+ 99 2. Using the sum of perfect squares formula: a 2+ b 2= (a + b) 2- 2ab Substitute a = 101 and b = 99 in the above formula: 101 2+ 99 2= (101 + 99) 2- 2(101)(99)​​​ = (200) 2- 2 (9999) = 40000 -19998 =20,002 Answer:101 2+ 99 2=20,002. Example 2:Find the sum of squares of the first 25 natural numbers. Solution: ...

In mathematics, the Fibonacci sequence is a Fibonacci numbers, commonly denoted F n . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci numbers are also strongly related to the nth Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as n increases. Fibonacci numbers are also closely related to Definition [ ] F n = F n − 1 + F n − 2 is valid for n> 2. The first 20 Fibonacci numbers F n are: F 0 F 1 F 2 F 3 F 4 F 5 F 6 F 7 F 8 F 9 F 10 F 11 F 12 F 13 F 14 F 15 F 16 F 17 F 18 F 19 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 History [ ] India [ ] F 7) ways of arranging long and short syllables in a cadence of length six. Eight ( F 6) end with a short syllable and five ( F 5) end with a long syllable. The Fibonacci sequence appears in m units is F m+1. Knowledge of the Fibonacci sequence was expressed as early as c.450BC–200BC). Singh cites Pingala's cryptic formula misrau cha ("the two are mixed") and scholars who interpret it in context as saying that the number of patterns for m ...

Perfect Square A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer. For example, 25 is a perfect square because it is the product of integer 5 by itself, 5 × 5 = 25. However, 21 is not a perfect square number because it cannot be expressed as the product of two same integers. In this article, we will discuss the concept of perfect squares and learn how to identify them. We will discuss the definition of a perfect square, its formula, and the list of perfect squares along with a few solved examples for a better understanding. 1. 2. 3. 4. 5. 6. 7. Perfect Square Formula Let us assume if N is a perfect square of a whole number x, this can be written as N = the product of x and x = x 2. So, the perfect square formula can be expressed as: Let us substitute the formula with values. If x = 9, and N = x 2. This means, N = 9 2 = 81. Here, 81 is a perfect square because it is the square of a whole number, 9. This can be understood in another way with the help of Perfect Square Trinomial: An 2= a 2 +2ab+b 2, and we get, (y+3) 2 = y 2 +6y+9. Here, y 2 +6y+9 is a 2 -8y+16 and 4x 2+ 12x +9. Perfect Squares List The table given below shows the perfect squares of the first 20 Natural Number Perfect Square 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144 13 169 14 196 15 225 16 256 17 289 18 324 19 361 20 400 Look at these lists of perfect squares 1-100 to have a better understanding of perfect squa...

Perfect Square:A number made by squaring a whole number. ora number that can be expressed as theproduct of two equal integers. For example:- • 9 is a perfect square because it can be expressed as 3× 3. • 16 is a perfect square because it can be expressed as 4× 4. • 25 is a perfect square because it can be expressed as 5× 5. Number 38 is not a perfect square number. Let,(2n + 1)is the odd number (assuming n ∈ N ) Squaring (2n + 1) ⇒ (2n+1) 2= 4n 2+ 4n +1 = (2n 2+ 2n) + (2n 2+ 2n + 1) Here, (2n 2+ 2n) and(2n 2+ 2n + 1) are twoconsecutive positive integers. H ence, it becomes clear that 25 is a perfect square,38 is not a perfect squareand the square of an odd number can always be written as sum of two consecutivepositive integers.