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The difference of square of two numbers is 45 and square of th

Question

The difference of square of two numbers is $45$ and square of the smaller is $4$ times the larger number. Find two numbers.

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The difference of square of two numbers is

45

and square of the smaller is

4

times the larger number. Find two numbers.

10 mins ago

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Text solutionVerified

Let

x

and

y

are two number where

x > y

then
according to question

x^{2} - y^{2} = 45

and

y^{2} = 4 x

from both equation

x^{2} - 4 x = 45

\Rightarrow x^{2} - 4 x - 45 = 0

\Rightarrow x^{2} - 9 x + 5 x - 45 = 0

\Rightarrow x (x - 9) + 5 (x - 9) = 0

\Rightarrow (x - 9) + (x + 5) = 0

\Rightarrow x - 9 = 0

\Rightarrow x = 9

Larger number

(x) = 9

square smaller number

= 4 \times 9 = 36

Smaller no.

\pm 36 \pm 6

Hence, number are

9, 6

9, 6

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Question Text	The difference of square of two numbers is $45$ and square of the smaller is $4$ times the larger number. Find two numbers.
Answer Type	Text solution:1
Upvotes	150