Evaluate:
Answer:
17) A
We know the general quadratic formula (a – b)² = a² – 2ab + b²
So we have,
(√5 – √2)² = (√5)² – [2 (√5) (√2)] + (√2)²
(√5)² – [2 (√5) (√2)] + (√2)² = 5 – 2√10 + 2 = 7 – 2√10
We know the general quadratic formula (a + b)² = a² + 2ab + b²
(√5 + √2)² = (√5)² + [2 (√5) (√2)] + (√2)²
(√5)² + [2 (√5) (√2)] + (√2)² = 5 + 2√10 + 2 = 7 + 2√10
So we have:
(√5 – √2)² (√5 + √2)² = (7 – 2√10) (7 + 2√10)
7(7 + 2√10) – 2√10(7 + 2√10)
49 + 14√10 – 14√10 – 40
49 – 40 = 9
