4. The sum of squares of two numbers is 208.
The square of the larger number is 18 times
the smaller number. Find the numbers.
Answers
Answer:
Explanation:
GIVEN ;-
⇒ Sum of Squares of two positive numbers are = 208
⇒Sum of larger number is 18 times the smaller number
TO FIND ;-
⇒ Find the two numbers = ?
SOL ;-
⇒ Let us take one of the number as x ,
⇒ Also the other number as y .
According to the question , { '' if the square of the larger number is 18 times the smaller number " }
So by this statement we can write as ,
⇒ x² = 18 y
⇒ x² + y² = 208 { because the sum of the squares of two positive integer is }208.
⇒ x² + y² = 208
⇒ Let us find the y
⇒18 y + y² = 208
⇒ y² + 18 y - 208 = 0
⇒ y² + 26 y - 8y - 208 = 0
⇒ y ( y + 26 ) - 8 ( y + 26 ) = 0
⇒ ( y+ 26 ) ( y - 8 ) = 0
But in the question it has been given that the integers are in the positive.
⇒ ( y - 8 ) = 0
⇒ y = 8
We got the value of one integer , now let us find the value of the another integer.......
x² + y² = 208
x² + ( 8 )² = 208
x² + 64 =208
x² = 208-64
x² = 144
x =√ 144
x = 12
So the two numbers are - 12 and 8