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  • The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Q7.    The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

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Given the difference of squares of two numbers is 180.

Let the larger number be 'x' and the smaller number be 'y'.

Then, according to the question:

x^2-y^2 = 180  and  y^2 = 8x

On solving these two equations:

\Rightarrow x^2-8x =180

\Rightarrow x^2-8x -180 = 0

Solving by the factorizing method:

\Rightarrow x^2-18x+10x -180 = 0

\Rightarrow x(x-18)+10(x-18) = 0

\Rightarrow (x-18)(x+10) = 0

\Rightarrow x=18,\ -10

As the negative value of x is not satisfied in the equation: y^2 = 8x

Hence, the larger number will be 18 and a smaller number can be found by,

y^2 = 8x putting x = 18, we obtain

y^2 = 144\ or\ y = \pm 12.

Therefore, the numbers are 18\ and\ 12  or  18\ and\ -12.

 

 

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Divya Prakash Singh

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