The sum of two numbers is 8 and the difference of the squares is 32 find the numbers

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If the difference of two number is 8 and the difference of their squares is 160. What are the numbers? Maths Q&A

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1

Two numbers are x and y such that x > y.Now,x + y = 50 ….(i)And,

y2 - x2 = 720

⇒ (y - x)(y + x) = 720⇒ (y - x)(50) = 720

⇒ y - x = 14.4 ….(ii)

Adding (i) and (ii), we get2y = 64.4

⇒ y = 32.2

Substituting the value of y in (i), we havex + 32.2 = 50⇒ x = 17.8

Thus, the two numbers are 17.8 and 32.2 respectively.

Page 2

Let the two numbers be x and y respectively.Then,x + y = 8 ….(i)⇒ x = 8 - yAnd,

`1/x + 1/y = 8/15`

⇒ `[ y + x ]/[xy] = 8/15`

⇒ `8/(xy) = 8/15` .....[ From(1) ]⇒ xy = 15⇒ ( 8 - y )y = 15

⇒ 8y - y2 = 15

⇒ y2 - 8y + 15 = 0
⇒ y2 - 3y - 5y + 15 = 0⇒ y( y - 3 ) - 5( y - 3 ) = 0⇒ ( y - 3 )( y - 5 ) = 0⇒ y = 3 or y = 5⇒ x = 5 or x = 3

Thus, the two numbers are 3 and 5 respectively.

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