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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 Two Numbers. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

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

#### Solution

Let the larger numbers be x

Then according to question,

Square of the smaller number be = 8x then

x2 - 8x = 180

x2 - 8x - 180 = 0

x2 - 18x + 10x - 180 = 0

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

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

x - 18 = 0

x = 18

Or

x + 10 = 0

x = -10

Since, being a positive integer so, x cannot be negative,

Therefore,

When x = 18 then smaller number be

sqrt(8x) = sqrt(8xx18)=sqrt144=+-12

Thus, two consecutive number be 18, 12 or 18, -12.

Is there an error in this question or solution?

#### APPEARS IN

Solution The Difference of Squares of Two Numbers is 180. the Square of the Smaller Number is 8 Times the Larger Number. Find Two Numbers. Concept: Solutions of Quadratic Equations by Factorization.
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