Number System Ques 32
Question
If the sum of three consecutive even perfect square number be 116 , what is the largest number?
(1) 4
(2) 16
(3) 100
(4) 144
(5) 64
(IBPS RRBs Officer CWE Prelim Exam, 31.12.2020)
Show Answer
Answer: (5)
Solution: (5)
$x^{2}+(x+2)^{2}+(x+4)^{2}=116$
$\Rightarrow x^{2}+x^{2}+4+4 x+x^{2}+16+8 x$ $=116$
$\Rightarrow 3 x^{2}+12 x+20=116$
$\Rightarrow 3 x^{2}+12 x-96=0$
$\Rightarrow x^{2}+4 x-32=0$
$\Rightarrow x^{2}+8 x-4 x-32=0$
$\Rightarrow x(x+8)-4(x+8)=0$
$\Rightarrow(x-4)(x+8)=0$
$\Rightarrow x=4$ and $x \neq-8$
$\therefore \quad$ Largest number $=(4+4)^{2}$ $=8 \times 8=64$
BETA
