Question

The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number. What is the greater number?

Answer 1

The greater number is 121

Step-by-step explanation:

The given is:

• The sum of 2 positive numbers is 151
• The lesser number is 19 more than the square root of the greater number

We need to find the greater number

Assume that the smaller number x and the greater number is y

∵ The smaller number is x and the greater number is y

∵ Their sum is 151

∴ x + y = 151 ⇒ (1)

∵ The lesser number is 19 more than the square root of the greater

   number

∴ x = 19 + √y ⇒ (2)

- Substitute x in equation (1) by equation (2)

∵ (19 + √y) + y = 151

- Subtract 151 from both sides and re-arrange the terms from

  the greatest power y

∴ y + √y - 132 = 0

Chang $\sqrt{y}$ to $y^{\frac{1}{2}}$ and substitute  $y^{\frac{1}{2}}$ by h

∵ $y^{\frac{1}{2}}$ = h

∴ y = h²

- Substitute each y by h

∴ h² + h - 132 = 0

- Factorize it into two factors

∴ (h - 11) (h + 12) = 0

- Equate each factor by 0 to find h

∵ h - 11 = 0

- Add 11 to both sides

∴ h = 11

∵ h + 12 = 0

- subtract 12 from both sides

∴ h = -12

∵ h = $y^{\frac{1}{2}}$

∴ $y^{\frac{1}{2}}$ = 11 and -12

∵ $y^{\frac{1}{2}}$ = √y

∴ √y = 11

∴ √y = -12 ⇒ rejected square root can't give -ve number

∴ √y = 11 only

- To find y square the both sides

∴ y = 121

The greater number is 121

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