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Question

The difference fo squares fo two numbers is 180. The square fo the smaller number is 8 times teh larger number. Find two numbers.
 


Solution

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= x squared
According to the question,
x squared minus 8 x equals 180 rightwards double arrow x squared minus 8 x minus 180 equals 0 rightwards double arrow x squared minus 18 x plus 10 x minus 180 equals 0 rightwards double arrow x left parenthesis x minus 18 right parenthesis plus 10 left parenthesis x minus 18 right parenthesis equals 0 rightwards double arrow left parenthesis x plus 10 right parenthesis left parenthesis x minus 18 right parenthesis equals 0 rightwards double arrow x equals 18 space o r space minus 10

Thus the larger number = 18 or -10.
Then, the square of the smaller number = 8 cross times 18 space space o r space space 8 cross times negative 10 equals 144 space o r space minus 80

But the square of a number can not be negative so the square of smaller number is  144.
Hence the smaller number is square root of 144 equals 12
Therefore the numbers are 12 and 18.

Mathematics
RD Sharma
Standard X

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