Solve Sqrt(2x^2-2x+1)-2x+3 = 0

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15 Apr 2014 Quadratic equation

Solve
Sqrt(2x^2-2x+1)-2x+3 = 0

OPtion

1) 1, 4
2) 3, 4
3) 1
4) 1, 6
5) 4
6) 5, 6
7) 2, 3
8) 6
9) 6, 8
10)None of these

Solution

Take square to get
2x^2 - 2x + 1 = 4x^2 + 9 - 12x
solve
x = 1, and x = 4
Put x = 1
Sqrt(2-2+1)-2+3 (not=) 0
Hence x = 1 is not a solution
for x = 4
Sqrt(2*4^2-2*4+1)-8+3 = Sqrt(32-8+1)-5 = Sqrt(25) - 5 = 5 - 5 = 0
The only root is x = 4
Option 5)

Correct Option: 5 Best Solution (12)

Ann Theressa   10 years AGO

Sqrt(2x^2-2x+1)-2x+3 = 0

Sqrt(2x^2-2x+1) = 2x-3

Squaring both sides

2x^2-2x+1 = (2x-3)^2

2x^2-2x+1 = 4x^2 - 12x + 9

2x^2 - 10x + 8 = 0

x^2 - 5x + 4 = 0

(x-4)(x-1) = 0

x = 1,4

checking the answers
when x = 4

Sqrt(2x^2-2x+1)-2x+3 = sqrt (32-8+1)-8+3
=sqrt(25) - 5
=5-5 = 0

when x = 1

Sqrt(2x^2-2x+1)-2x+3 = sqrt (2-2+1)-2+3
=sqrt(1) +1
=1+1 = 2 (not equal to zero)

So x = 4 is the solution

Like? Yes (7) | No (4)  

Santosh Vishwakarma   10 years AGO

put the value.

Like? Yes (1) | No   

Charu jain   10 years AGO

Put options in the equation on putting 4 we can have equation like
5-8+3 =0

Like? Yes (1) | No   

Udhaya kumar   10 years AGO

1,4 will be find through given eqn.
bt 1 doesn't satisfy abv eqn...
hence 4 will be only answer........

Like? Yes (2) | No (1)  

S M ANIRUDH   10 years AGO

Verify the options

Like? Yes (1) | No   

RAKESH   10 years AGO

Sqrt(2x^2-2x+1)-2x+3 = 0
=> 2x^2-2x+1=(2x-3)^2
=> x^2-5x+4=0
=> x = 1,4
but x=1 doesn't satisfy given eqn

x=4 only

Like? Yes (1) | No (1)  

ASHISH MITTAL   10 years AGO

After solving we got x=1 and 4 but x=1 is not satisfying the condition so x=4 and option no (5)

Like? Yes (1) | No (1)  

Sudipta Mukherjee   10 years AGO

from the answer ...Only x-4 satisfy the equation...

Like? Yes (1) | No (1)  

arnold   10 years AGO

substitute option 5 in equation we get
LHS=RHS

Like? Yes (1) | No (1)  

Rahul Das   10 years AGO

just put the value x=4 you will get get answer coming =0

Like? Yes (1) | No (1)  

NIRUPOM GHOSH   10 years AGO

soln:sqrt(2x^2-2x+1)=2x-3
both sides squares then solve:(2x^2-2x+1)=(2x-3)^2
we get x=1,4 but x=1 not satisfy the eqn: sqrt(2x^2-2x+1)-2X+3=0 so x=4.

Like? Yes (1) | No (1)  

KAUSTUBH BHARDWAJ   10 years AGO

becz. only 4 is the solution of above eqn.by hit n trial method

Like? Yes (1) | No (2)