Question

the difference of the squares of of two number is 180 the square of the smaller number is 8 times the larger number find the two number ​

Answer 1

Answer:

numbers = 18 & 12

Step-by-step explanation:

let the largest number be 'n'

and smallest be 'x'

according to question

${x}^{2} = 8n$

and

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

put

${x}^{2} = 8n \: \: \: \: \: \: \: \: \: \: \: in \: \: the \: \: \: {eq}^{n}$

now it becomes

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

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

by solving the above quadratic equation we get

$(n - 18)(n + 10) = 0$

so,

n = 18

$n = 18 \\ {x}^{2} = 8n = 8 \times 18 \\ {x}^{2} = 144 \\ x = 12$

therefore numbers are 18 & 12

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Verification

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

after putting the values

${18}^{2} - {12}^{2} = 180 \\ 324 - 144 = 180 \\ 180 = 180 \\ lhs = rhs$

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