Question

The sum of two numbers is 17and the sum of their squares is 157.Find the numbers.

Answer 1

let the no. be x and (17-x)
so acc to your question
x+(17-x) = 17
x sq+(17-x) sq=157
x sq +289+x sq -34x = 157
2x sa +289-157-34x =0 so by applying the factorization method u will get two values of x
one is positive and other is negative so we will prefer the positive one ...
hope it will help you

Answer 2

Heya..

I'm here to help you..

Let two numbers be x and y.

According to question,

=) x + y = 17

And

(x^2 + y^2) = 157

=) (x+y) = 17

Squaring both sides,

=) (x+y) ^2 = 17^2

=) x^2 + y^2 + 2xy = 289

=) 157 + 2xy = 289

=) 2xy = 289 - 157

=) 2xy = 132

=) xy = 132/2

=) xy = 66


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Since (x-y) ^2 = x^2 + y^2 - 2xy

= 157 - 2(66)

= 157 - 132

= 25

Hence (x-y) = 5.....

At last we get two equations,

=) x+y = 17 and

x-y = 5

-------------

Add both equations,

=) x+ y + x - y = 17 + 5

=) 2x = 22

=) x = 22/2

=) x = 11..

Put its value to find y.

=) x-y = 5

=) 11 - y = 5

=) 11-5 = y

=) 6 = y..

Hence x = 11 and y = 36.

Hope it's helpful to u.