Question

(2x-3)=root2x^2-2x+21

Answer 1

$\textbf{Given:}$

$\sqrt{2x^2-2x+21}=2x-3$

$\textbf{To find:}\;x$

$\sqrt{2x^2-2x+21}=2x-3$

$\text{Squaring on both sides, we get}$

$2x^2-2x+21=(2x-3)^2$

$2x^2-2x+21=4x^2+9-12x$

$\text{Rearranging terms, we get}$

$2x^2-10x-12=0$

$x^2-5x-6=0$

$x^2-6x+x-6=0$

$x(x-6)+1(x-6)=0$

$(x+1)(x-6)=0$

$x=6,-1$

$\text{But x=-1 is not permissible}$

$\therefore\textbf{The solution is x=6}$

Find more:

Solve the following quadratic equations by factorization:(x+3/x-2)-(1-x/x)=17/4

https://brainly.in/question/15926221

Answer 2

Answer:

6 or -1

Step-by-step explanation:

(2x-3) ^2=√2x-2x+21

4x^2-12x+9= 2x^2-2x+21

4x^2-2x^2-12x+2x+9-21=0

2x^2-10x-12=0

D= (-10) ^2-4×2×-12

D=196

by quadratic formula:

x=10+_√196/2×2

x= 10+_14/4

x= 24/4 or -4/4

x= 6 or -1