Question

7. 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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Answer 1

Step-by-step explanation:

Let the two numbers ne x and y

Given

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

Also given

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

Hence we have

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

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

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

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

$x = 18 \: or \: - 10$

when x=18

$y ^{2} = 8 \times {18} = 144$

Hence y= ±12

when x=-10

${y}^{2} = 8 \times - 10 = - 80$

Hence y=±i√80

Important Note. If you are not aware of imaginary numbers (Grade 8 or below) please ignore the solutions for x=-10.

Answer 2

Answer:

this is your ans

I hope it helps