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

M4maths Previous Puzzles

12 Sep 2013 Quadratic Equation

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

OPtion

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

Solution

The equation can be written as
sqrt(2x^2-2x+1)=2x-3
Squaring both side
(2x^2)-2x+1=(4x^2)+9-12x
Solve we get
x=1 or x=4
But 1 is not satisfy the LHS side of the equation (By checking)
and 4 is satisfy the LHS side of the equation
so The only root is x = 4
option 2

Correct Option: 2 Best Solution (11)

Mayuresh Srivastava   11 years AGO

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

squaring both sides and on solving further
x^2-5x+4=0
x=1,x=4 but x=1 is not satisfying so x=4.

Like? Yes (9) | No   

Ezhilarasi   11 years AGO

while subs.x=4, we get,
sqrt[2(4)^2-2(4)+1]-2(4)+3=0
sqrt[32-8+1]-8+3=0
sqrt[25]-5=0
5-5=0
0=0
LHS=RHS

Like? Yes (3) | No   

TEJ PRAKASH TEWARI   11 years AGO

sqrt(2x^2-2x+1)=2x-3
Use hit n trial method.And select a value for x for which u can calculate sqrt(x^2-2x+1).
here x=1,2,3 do not satisfy the condition
put x=4 => lhs=rhs
x=5(does not satisfy the condition.)
Ans. x=4

Like? Yes (1) | No   

kudumula chethana reddy   11 years AGO

Square both sides of equation after sending -2x+3 to right hand side . It is actually 4 or 1 but 1 doesnt satisfy the given equation

Like? Yes (1) | No   

ankit rawat   11 years AGO

(2x^2-2x+1)=(2x-3)^2
solving we get x= 1 and x=4
but we know that value inside square has to be positive and the term (-2x+3) gives +1 so for x=1 function can not be zero
so only root is x = 4

Like? Yes (1) | No   

Chithra   11 years AGO

Sqrt(2(4)^2-2(4)+1)-2(4)+3
sqrt(32-8+1)-8+3
sqrt(25)-5
5-5=0
so ans x=4

Like? Yes (1) | No   

ABHISHEK KUMAR MISHRA   11 years AGO

given that (2x^2-2x+1)^1/2 -2x+3=0
or (2x^2-2x+1)^1/2 = 2x-3
here 2x-3>0 so that x>=3/2......(1)
now according to question:
(2x^2-2x+1)^1/2 = 2x-3
squaring both side
(2x^2-2x+1) = (2x-3)^2
x^2-5x+4=0
(x-4)(x-1)=0
here x=4,1
but according to (1) x>=3/2
so that x=4 answer

Like? Yes (1) | No   

Rashmi bharti   11 years AGO

we have x=1,2,3,4and 5.
putting x=1,the equation would be 4-2=0,
similarly x=4,we get sqrt(2*4^2-2*4+1)-2*4+3=0
so, 5-8+3 i,e. 0.so ans is x=4.

Like? Yes (1) | No (1)  

nagashree   11 years AGO

by hit and trial nly 4 satisfies

Like? Yes (1) | No (1)  

mohini gupta   11 years AGO

sqrt(2(4*4)-2*4+1)-2*4+3=0

Like? Yes (1) | No (1)  

praveen sb   11 years AGO

by trial n error method we wen X=4
sqrt(2*16-2*4+1)-8+3=5-8+3=0
and hence option 2 is right

Like? Yes (1) | No (2)