The sum of the squares of two positive integers is 208. If the square of large number is 18 times the smaller number. Find the numbers. ANSWER WILL BE MARKED AS BRAINLIEST
Answers
Answer:
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
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