Question

A natural number is greater than another natural number by 3 the sum of their square is 89 find them

Answer 1

Let the two no.s be 'x' and 'y'

Given,

x = y + 3                → 1

     x + y = 89

y + 3 + y = 89               (From 1)

   2y + 3 = 89

         2y = 89 - 3

           y = 86 ÷ 2

      ⇒ y = 43

x = y + 3 = 43 + 3

∴ x = 46.

Answer 2

The two numbers is 5 and 8.

• Let the natural number be x.

• Other natural number x+3.

• According to the given condition,

$x^{2}$  + ${(x+3)}^{2}$ = 89

• We have to find the roots of the quadratic equation,

$x^{2} + x^{2} + 6x + 9 =89$

$2x^{2} +6x +9 =89$

$2x^{2} +6x -80 = 0$

• Using the formula to find the roots of the equation ,

x = $\frac{-b+\sqrt{b^{2}-4ac } }{2a}$ and x = $\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

x = $\frac{-6+\sqrt{6^{2}-4(2)(-80) } }{2(2)}$ and x = $\frac{-6-\sqrt{6^{2}-4(2)(-80) } }{2(2)}$

x = $\frac{-6+\sqrt{6^{2}-4(2)(-80) } }{2(2)}$ and x = $\frac{-6-\sqrt{6^{2}-4(2)(-80) } }{2(2)}$

x = $\frac{-6 + 26}{2(2)}$ and x = $\frac{-6- 26 }{2(2)}$

x = $\frac{20}{4}$ and x = $\frac{-32}{4}$

x = 5  and x = -8

• x= 5 is the solution
•  x= -8 is not a natural number so it is not the solution.
• Other number will be x + 3 = 8