The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
Answers
SOLUTION :
Let x be the larger number & square of a smaller number be 8x .
A.T.Q
Square of a larger number - Square of a smaller number = 180
x² - 8x = 180
x² - 8x - 180 = 0
x² - 18x + 10x - 180 = 0
[By middle term splitting]
x(x - 18) + 10(x - 18) = 0
(x - 18) (x + 10) = 0
(x - 18) = 0 or (x + 10) = 0
x = 18 or x = - 10
Case 1 :
If x = 18 , then square of a smaller number = 8x = 8 × 18 = 144
Smaller number = √144 = ± 12
Case 2 :
If x = - 10 , then square of a smaller number = 8x = 8 × -10 = - 80
This is not possible as square of a number cannot be negative.
Hence, the two numbers are (18 , 12) & (18 , - 12) .
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Answer:
the numbers are 18 and 12
Step-by-step explanation:
Let the larger no be x and smaller no be y
Therefore x²-y²=180
And y²=8x
Thus by substituting y²=8x in the first equation
x²-8x-180=0
x²-18x+10x-180=0
x(x-18)+10(x-18)=0
Therefore x=18 or x=-10
If x=18 then y=√18x8=12
If x=-10 then y=√-10x8=√-80 which is not possible