Question

The sum of the squares of 2 consecutive nos is 145.find the consecutive nos

Answer 1

145=The sum of:

72+73=145

72,73 are consecutive natural numbers

Answer 2

$\bf{Answer:-}$

• Let one of the number be x.

So, the next consecutive number is x+1.

$\bf{Given:-}$

The sum of the squares is 145.

$\implies$ $\sf{x^2 + (x+1)^2 = 145}$

$\implies$ $\sf{x^2 + x^2 + 2x + 1 = 145}$

$\implies$ $\sf{2x^2 + 2x - 144 = 0}$

• $\sf{Now\: Dividing\:by\:2,\:we\:get:-}$

$\sf{x^2 + x - 72 = 0}$

$\bf{Now,\:we\:will\:do\:factor:-}$

$\implies$$\sf{(x +9) ( x-8) = 0}$

$\implies$ $\sf{x1= -9 \longrightarrow\: x1+1 = -8}$

$\implies$ $\sf{x2= 8 \longrightarrow\: x2+1 = 9}$

★ Hence, the numbers are 8 and 9 or we can say (-8 and -9)