Question

ind two numbers such that the sum of their squares is 100. The square of the larger number is equal to the sum of the product of the larger numberand four times the smaller number and eight times the larger number.

Answer 1

Answer:

$a=\sqrt\frac{120}{13}$

$b=\frac{-7}{4}\sqrt \frac{120}{13}$

Step-by-step explanation:

Let the larger number is a and the smaller number is b.

According to the question,

a² + b² = 100 .... (1)

And

a² = a (4b + 8a)

a = 4b + 8a

b = -7a/4    ..... (2)

Put in equation (1)

$a^{2}+\left ( \frac{-7a}{4} \right )^{2}=100$

65a² = 100 x 16

$a^{2}=\frac{600}{65}$

$a=\sqrt\frac{120}{13}$

Put in equation (2)

$b=\frac{-7}{4}\sqrt \frac{120}{13}$