In the following equation, solve for x: √(2)x-√(3)=√(5) (4 marks)

Question

In the following equation, solve for x:
`√(2)x-√(3)=√(5)`
(4 marks)

Answer 1

First we can add
`√(3)` to both sides:


`x √(2) = √(5) + √(3)`

Next we can divide both sides by
`√(2)`:


`x = ( √(5) + √(3) )/( √(2) )`

Finally, we can rationalize the denominator by multiplying the numerator and denominator by
`√(2)`:


`( √(5) + √(3) )/( √(2) ) * ( √(2) )/( √(2) )`


`( √(2)(√(5) + √(3)) )/( 2 )`


`x = ( √(10) + √(6) )/( 2 )`