Question

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.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

According to question:-

Let the larger number be x

Smaller number be y

${x}^{2} - {y}^{2} = 180 \: \: (1)$

${y}^{2} = 8x \: \: (2)$

$Substituting \: \: y^2=8x \: \: in \: \: (1)$

${x}^{2} - 8x = 180$

Using factorisation method:-

${x}^{2} - 8x - 180 = 0$

Product= -180

Sum= -8

Numbers= -18, 10

Splitting the mid term:-

${x}^{2} - 18x + 10x - 180 = 0$

$({x}^{2} - 18x) + (10x - 180) = 0$

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

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

x+10=0 or x-18=0

x= -10,18 (but x cannot be negative)

x=18

Larger number =18

Substituting the value of x in (2)

${y}^{2} = 18 \times 8$

${y}^{2} = 144$

$y = \sqrt{144}$

y=12

Verification by substituting the value of and y in (1).

${18}^{2} - {12}^{2} = 180$

324-144=180

180=180

Since, LHS=RHS

Hence, The given solution:-

Larger number=18

Smaller number=12