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the difference of squares of two numbers is 180. the square of smaller no. is 8 times the larger number. find the two numbers .

Let the larger number = x

Then the square of the smaller number = 8 times the larger number = 8x

and the square of the larger number = x2

According to the question,

  x2 - 8x = 180

  =>  x2 - 8x - 180 = 0

  =>  x2 - 18x + 10x - 180 = 0

  =>  x(x - 18) + 10(x - 18) = 0

  =>  (x - 18) (x + 10)  = 0

  =>  x - 18 = 0  or x + 10 = 0

  =>  x = 18  or x = -10

Thus, the larger number = 18 or -10

Then, the square of the smaller number  = 8(18)  or     8(-10)

  = 144       or     -80

The square of a number can't be negative, so, the square of smaller number = 144

Hence, the smaller number = sqrt(144) = 12

The numbers are 12 and 18

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  • -31
the difference of two square numbers is 144. if the smaller number is 5. find the larger number
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The answer is not apt bcoz the the square must be 8x²
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joshua ur question answer
a2-b2=144
given b2=25
therefore a2=144+25=165
a=13
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X^2-y^2=180 Y^2=8x x^2-8x-180=0 x^2-18x+10x-180=0 x(x-18)10(x-18)=0 (x+10)(x-18) X=18 , x=-10
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Do it for your self i am a beast
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Let larger no.be X,then Square of smaller no. will be 8x. Square of larger no .=x^2 A.T.Q: X^2-8x=180 x^2-18x+10x-180=0 (x-18)(X+10) X=18,-10 X=18,it is larger no. Smaller no. Will be 10,√8•18=√144=12)
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let the the two numbers be x and y
so x(square)-y(square)=180
now according to the question square of the smaller number(y) minus 8times the larger number only (x) and not x(square)
so: y^2=8x
equation:x^2-y^2=180
in place of y^2 we can write 8x
so.... x^2-8x-180=0 
solve it by split method or the b(square) wala formula

hope you find this answer helpfull
 
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Let the larger number = x Then the square of the smaller number = 8 times the larger number = 8x and the square of the larger number = x2 According to the question, x2 - 8x = 180 => x2 - 8x - 180 = 0 => x2 - 18x + 10x - 180 = 0 => x(x - 18) + 10(x - 18) = 0 => (x - 18) (x + 10) = 0 => x - 18 = 0 or x + 10 = 0 => x = 18 or x = -10 Thus, the larger number = 18 or -10 Then, the square of the smaller number = 8(18) or 8(-10) = 144 or -80 The square of a number can't be negative, so, the square of smaller number = 144 Hence, the smaller number = sqrt(144) = 12 The numbers are 12 and 18
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