The sum of the real solutions of equation 2≤ft|x|²+51=≤ft|1+20x| is

Correct Answer is : None of these

Correct Answer is : None of these

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CGPET 2015 Solved Paper

Section: Mathematics

Question : 101 of 150

Marks: +1, -0

2\left|x\right|^2+51=\left|1+20x\right|

Solution:

Given,

2\left|x\right|^2+51 = \left|1+20x\right|

Then, following two possible cases arises :

Case I When

1+20x > 0 \Rightarrow x>\frac{-1}{20}

∴

2x^2+51 = (1+20x)

⇒

2x^2-20x+50=0

⇒

x^2-10x+25=0 \quad [\because 2\neq 0]

⇒

(x-5)^2=0

⇒

x=5,5

Case II When

1+20x \Rightarrow x < \frac{-1}{20}

∴

2x^2+51=-(1+20x)

⇒

2x^2-20x+52=0

⇒

x^2-10x+26=0

Here,

D<0

Thus, roots are imaginary.

Hence, sum of real roots

=5+5=10

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