Question

find a number such that if 5,15 and 35 are added to it ,the product of the first and third result may be equal t the square of the second?

Answer 1

let the number be x

According to question.
(5+x) (35+x) = (15 + x )²

or, 5(35+x)+x(35+x) = (15)²+x²+2(15)(x)
[(a+b)²=a²+b²+2ab]

or, 175+5x + 35x + x² = 225+x²+30x

or, 175+40x+x²= 225+x²+30x

or, 175+40x-30x = 225+x²-x²

or, 175+10x = 225

or, 10x = 225-175

or, 10x = 50

or, x = 50/10

or, x = 5

Answer) The number is 5.
Proof-
(5+5)(35+5) = (15+5)²

or, 10×40 = (20)²

or, 400 = 400
Hence, LHS = RHS.
proved.