A man’s age after 15 years will be the square of his age 15 years ago. Find
the age using completing the square method.
Answers
Answer:
hope it helps you..............
Man's present age is 21 years .
Given :
A man's age after 15 years will be the square of his age 15 years ago.
To find out : Man's present age.
Solution : We are given information that a man's age after 15 years will be the square of his age 15 years ago.
Depending on this information , we will have to frame an equation.
Let present age of a man is x years.
After 15 years his age will be ( x + 15) years.
15 years ago his age was ( x - 15 ) years.
According to the given information , the equation will become ,
( x + 15 ) = ( x - 15 )²
here we will be using the formula
( a - b )² = a² - 2ab + b²
a = x, b = 15
therefore by solving
( x - 15 )² = x² - 2 x 15 x X - (15)²
= x² - 30x -225
hence
( x + 15 ) = x² - 30x - 225
putting the x terms together we get
x² - 30x - x = -225 + 15
x² -31 x = - 210
Adding ( 31/2)² both the sides
x² -31 x + 31/2)² = 210 - ( 31/2)²
( x - 31/2 ) ² = 210 - 961/4
( x - 31/2 ) ² = (840 - 961 ) /4
(x - 31/2 ) ² = 121/4
Taking square root both the sides
x - 31/2 = + 11/2 or - 11/2
solving we get
x = 21 or x = 10
x = 10 is not possible so x = 21 is the correct solution.
Hence Man's present age is 21 years .
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