Question

Sum of two numbers is 17, whereas sum of their squares is 145. What is the product of the two numbers?

Answer 1

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Solution==>>

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x +y =17 also y = 17-x

x² + y² = 145

x² +(17-x)² = 145

x² +289 -34x +x² = 145

2x² -34x +144 = 0

(2x -16)(x-9) = 0

x =8

So if x =8 then y = 9


So , Product is

8×9=72

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Verification==>

Their sum is 17

8+7=17

and

sum of square is 145

(8)²+(9)²

64+81=145
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Answer 2

Let the two numbers be x and y

x + y = 17

x^2 + y^2 = 145

x^2 + (17-x)^2 = 145

x^2 + x^2 - 34x + 289 = 145

2x^2 - 34x + 144 = 0

x^2 - 17x + 72 = 0

x^2 - 9x - 8x + 72 = 0

x(x - 9) -8 (x-9) = 0

x = 8 or x = 9

If x = 8, y = 9

When x = 9, y = 8

Product = 8*9 = 72.