SSC CHSL 9 Jan 2017 Shift 3 Paper

Question : 56 of 100

Marks: +1, -0

What is the value of 2 consecutive natural numbers, sum of whose squares is 145?

Solution:

Let the consecutive natural numbers be

(x)

and

(x+1)

Sum of squares =

(x)^2 + (x + 1)^2 = 145

⇒

x ^2 + x^2 + 2x + 1 = 145

⇒

2x^2 + 2x − 144 = 0

⇒

x^2 + x − 72 = 0

⇒

x^2 + 9x − 8x − 72 = 0

⇒

x(x + 9) − 8(x + 9) = 0

⇒

(x − 8)(x + 9) = 0

⇒

x = 8, −9

Since,

x

is a natural number, it can't be negative.
∴ The natural numbers are 8 and 9

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