Theory question 101
Indices(a) Solve 1/81(x−2) = 27(1−x)
(b) Simplify 5/(√7 − √3) + 1/(√7 − √3) leaving your answer in surd form
Show the model answer
Model answer
(a) 3−4(x−2) = 33(1−x), so −4x + 8 = 3 − 3x and x = 5.
(b) Both fractions have the same denominator: 6/(√7 − √3).
Multiply top and bottom by √7 + √3: 6(√7 + √3)/(7 − 3) = 3(√7 + √3)/2.
Explanation
Rationalise by multiplying by the conjugate √7 + √3.