Theory question 107
Algebraic Expressions(a) Given that p = x + ym3, find m in terms of p, x and y.
(b) Using the method of completing the square, find the roots of the equations x2 − 6x + 7 = 0, correct to 1 decimal place.
(c) The product of two consecutive positive odd numbers is 195. By constructing a quadratic equation and solving it, find the two numbers.
Show the model answer
Model answer
(a) ym3 = p − x, m3 = (p − x)/y, m = ∛((p − x)/y)
(b) x2 − 6x = −7; add 9: (x − 3)2 = 2
x − 3 = ±√2 = ±1.414, x = 4.4 or 1.6
(c) Let the numbers be n and n + 2: n(n + 2) = 195
n2 + 2n − 195 = 0, (n − 13)(n + 15) = 0
n = 13 (n = −15 rejected, not positive); the numbers are 13 and 15
Explanation
To complete the square, add (half the coefficient of x)² to both sides.