Question

Solve.
sqrt(x+7) - sqrt(2x-3)=2

Answer 1

By looking if I put x = 2 :

Then :

\[\sqrt{2+7} - \sqrt{2(2)-3} \implies \sqrt{9} - \sqrt{1} = 3 - 1 = \color{green}{2}\]

Answer 2

So, here one solution will be 2..

Answer 3

thank you! but why did you choose 2?

Answer 4

This will take real time when it will be solved..

Otherwise,I try it for you..

Answer 5

Bring one square root term to the right hand side by adding \(\sqrt{2x-3}\) to both the sides..

Answer 6

i did that and the i put it by ^2 to cancel the sqrt in the other side...but i keep getting different answers.

Answer 7

\[\sqrt{x+7} = 2 + \sqrt{2x-3}\]
Now square both the sides :

\[x+7 = (2 + \sqrt{2x-3})^2\]
\[x+7 = 4 + 2x - 3 + 2 \cdot 2 \cdot \sqrt{2x-3}\]
\[-x + 6 = 4 \cdot \sqrt{2x-3}\]

Answer 8

Take the square now again :

\[(-x+6)^2 = (4 \cdot \sqrt{2x-3})^2 \implies 36 + x^2 - 12x = 16(2x-3)\]

Answer 9

This will come out to be as :

\[36 + x^2 - 12x = 32x - 48 \implies \color{red}{x^2 - 44x + 84 = 0}\]

Answer 10

ohhh okay i got it. thank you!!

Answer 11

You are welcome dear...

Answer 12

You can simply look here : \(x^2 - 44x + 84 = 0\)

2 is satisfying this equation : \(2^2 - 44 \times 2 + 84 \implies 4 - 88 + 84 \implies \color{green}{0}\)

Answer 13

thanks=D