Question

the sum of squares of two positive integer is 117.if the squares of the smaller number equals four times the larger number,find the integer

Answer 1

Answer:

Step-by-step explanation:

Let the square of the smaller number be x.

The square of the larger number will be :

117 - x

Given that the square of the smaller number is four times the larger number we have :

Larger number = x/4

Now we can square the larger number :

(x/4)^2 = 117 - x

x^2/16 = 117 - x

x^2 = 16(117 - x)

x^2 = 1872 - 16x

This forms a quadratic equation.

x^2 + 16x - 1872 = 0

We will use quadratic formula in this case :

x = {-16 +/- square root (16^2 + 4 × 1872)} / 2

= {-16 +/- 88}/2

x = 36 or - 52

We take 36 since it is positive.

The square of the smaller number is 36.

The square of the larger number is :

117 - 36 = 81

The integers are thus :

6 and 9

Since :

Square root of 36 = 6

Square root of 81 = 9

Answer 2

Answer:

Step-by-step explanation:

Pls find the attachment

It is done in the form of quadratic equation and not the linear equation in two variables.

Hope it is helpful!!!