Question

A number is 7cm less than another number. If the sum of their squares

169 find the numbers.​

Answer 1

$\huge \fbox \red{Answer : 12 and 5}$

Let, the numbers be x and y

According to 1st case :

x = y + 7

x - y = 7 ... (1)

According to 2nd case :

x^2 + y^2 = 169 ... (2)

As we know that :

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

From equation (1) and (2) :

=> 169 = 7^2 + 2xy

=> 169 = 49 + 2xy

=> 2xy = 169 - 49 = 120

=> xy = 60 .... (3)

From equation (1) and (3) :

x - 60/x = 7

=> x^2 - 7x - 60 = 0

=> x^2 - 12x + 5x - 60 = 0

=> x(x - 12) + 5(x - 12) = 0

=> (x - 12)(x + 5) = 0

Required values of x = 12 and -5

Since the negative value is not acceptable so the value of x will be 12

On putting the value of x in equation (1) :

12 - y = 7

=> y = 12 - 7 = 5

So, the numbers will be 12 and 5 ✔✔

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Hope it helps ☺

Fóllòw Më ❤