Question

Find two consequtive natural number , the sum of whose square is 145

Answer 1

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$\huge\boxed{SOLUTION}$

➡️Let one number be x

➡️Then other number = x+1

➡️It i s given that the sum of square of those numbers is 145.

Therefore, 
x² + (x+1)² = 145.
x² + x² + 2x + 1 = 145      

       {(a+b)²= a² + 2ab + b²}

2x² + 2x - 144 = 0 

➡️Dividing both sides by 2, we obtain

x² + x - 72 = 0

x² - 8x + 9x - 72 = 0

x(x-8) + 9 (x-8) = 0

(x+9) (x-8) = 0

x = -9  or x=8 

As x = -9 can't be answer because it is not a natural number.

➡️Hence, x = 8.

➡️And, x+1 = 9.

➡️$\underline{Justification:-}$

                         8² + 9²
                       = 64 + 81 = 145

➡️Hence, it is proved.