Theory question 101
Surds(a) Given that (√3 − 5√2)(√3 + √2) = a + b√6, find a and b.
(b) If (21−y × 2y−1)/2y+2 = 82−3y, find y.
Show the model answer
Model answer
(a) Expand: 3 + √6 − 5√6 − 5 × 2 = −7 − 4√6, so a = −7 and b = −4.
(b) Left side = 2(1 − y) + (y − 1) − (y + 2) = 2−y − 2; right side = 23(2 − 3y) = 26 − 9y.
−y − 2 = 6 − 9y → 8y = 8 → y = 1.
Explanation
Write everything as a power of 2 and equate the indices.