Question

The difference of sq of two numbers is 180. The sq of the smaller no. is 8 times the larger no. find the two no.

Answer 1

hii here is ur solution

Let the larger and smaller no. be and y
xsq - ysq = 180 and ysq = 8x

xsq - 8x = 180

xsq - 8x - 180= 0

xsq - 18x + 10x - 180 = 0

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

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

x= 18, -10


the larger no. cannot be negative as 8 times of the larger no. will be negative and hence, the sq of the smaller no. will be negative which is not possible.

# the larger no. will be 18
x= 18

## ysq = 8x = 8* 18 = 144

>> y = + - root 144 = + - 12

s
smaller no. = + - 12

there fore, the no. are 18 and 12 or 18 and -12

hope it helps you..

Answer 2

$let \: the \: two \: numbers \: be \: x\: \: and \: y \\ as \: per \: the \: question \\ {x}^{2} - {y}^{2} = 180 \\ and \\ {y}^{2} = 8x - - - - - (1) \\ now from(1) \\ {x}^{2} - 8x - 180 = 0 \\ = > {x}^{2} - 18x + 10x - 180 = 0 \\ = > x(x - 18) + 10(x - 18) = 0 \\ = > (x - 18)(x + 10) = 0$
now, if x-18=0, then x=18


if x+10=0, then x=-10


but x is not equals to -10 because 8×(-10)= -80 and the square root of it is imaginary.



so, x=18


from (1),


${y}^{2} = 8 \times 18 \\ = > {y}^{2} = 144 \\ = > y = 12$
so, x=18 and y=12



here is the answer to your question