Find a number such that if 5, 15, and 35 are added to it, the product of the first and third
maybe equal to the square of the

1 thought on “Find a number such that if 5, 15, and 35 are added to it, the product of the first and third<br />maybe equal to the square of the”

1. Answer:

   Number = 5

   Step-by-step explanation:

   Let the number = x

   Number + 5 = x + 5

   Number + 15 = x + 15

   Number + 35 = x + 35

   Product of the first and third = (x + 5)(x + 35)

   By the identity, (x+y)(u+v) = xu+xv+yu+yv, we get

   (x + 5)(x + 35) = x² + 35x + 5x + 175 = x² + 40x + 175

   Square of the second = (x + 15)²

   By the identity, (a+b)²=a² + 2ab + b², we get

   (x + 15)² = x² + (2 × x ×15) + 15² = x² + 30x + 225

   It is given that,

   Product of the first and third = Square of the second

   x² + 40x + 175 = x² + 30x + 225

   x² + 40x = x² + 30x + 225 – 175 = x² + 30x + 50

   x² + 40x – 30x = x² + 50

   x² + 10x = x² + 50

   x² – x² + 10x = 50

   10x = 50

   x = 50 ÷ 10 = 5

   So the answer is 5.

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