Question

Solve for x: under root 6x+7 - (2x-7) =0

Answer 1

√(6x + 7) - (2x -7) =0


√(6x + 7) = (2x -7)

take square both sides

6x + 7 = (2x - 7)^2 = 4x^2 -28x +49

4x^2 -34x +42 =0

2x^2 -17x +21 =0

2x^2 -14x -3x +21 =0

2x(x - 7) -3(x - 7) =0

(2x -3)(x - 7) =0

x = 3/2 and 7

Answer 2

$\bf\huge\textbf{\underline{\underline{Answer :-}}}$    

${\boxed{\bigstar{sf\:{We\:have\:to\:Find}}}}$

$\tt{\implies\sqrt{6x + 7} - (2x - 7) = 0}$  

$\tt{\implies\sqrt{6x + 7} = (2x - 7)}$

$\textbf{\underline{\underline{Squarring both Sides :-}}}$    

$\tt{\implies 6x + 7 - (2x - 7)^2 = 0}$

$\tt{\implies 6x + 7 = 4x^2 + 49 - 28x$

$\tt{\implies 4x^2 - 34x + 42 = 0}$

$\tt{\implies 2x^2 - 17x + 21 = 0}$

$\textbf{\underline{\underline{Quadratic Formula :-}}}$  

$\sf{\implies x = \dfrac{17 + \sqrt{17^2 - (4\times 2\times 21)}}{2\times 2}$  

$\sf{\implies x = \dfrac{17 + \sqrt{289 - 168}}{4}$

$\sf{\implies\dfrac{17 + \sqrt{121}}{4}$

$\sf{\implies x = \dfrac{17 + 11}{4}$

$\sf{\implies x = \dfrac{28}{4} , \dfrac{6}{4}}$

${\boxed{\bigstar{\sf\:{Hence\:we\:get\:x\:=\:7\:and\:1.5}}}}$