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Anettt [7]
3 years ago
7

Find 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 o

f the larger numberand four times the smaller number and eight times the larger number.
Mathematics
1 answer:
Shtirlitz [24]3 years ago
3 0

Answer with Step-by-step explanation:

Let x and y are two  numbers

According to question

x^2+y^2=100....(1)

Suppose x is larger than y

x^2=x(4y+8x)

x=4y+8x

x-8x=4y

-7x=4y

y=-\frac{7}{4}x

Substitute the value of y

x^2+(-\frac{7}{4}x)^2=100

x^2+\frac{49}{16}x^2=100

\frac{16x^2+49x^2}{16}=100

\frac{65}{16}x^2=100

x^2=\frac{16\times 100}{65}

x=\sqrt{\frac{1600}{65}}=\frac{40}{\sqrt{65}}=\frac{40}{65}\sqrt{65}=\frac{8}{13}\sqrt{65}

y=-\frac{7}{4}\times \frac{8}{13}\sqrt{65}=-\frac{14}{13}\sqrt{65}

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