Question
If a and b are two real numbers such that b > a, ab < 0,
the sum of their squares is 458 and the difference between their squares is 120, then find the value of a - b.Solution
a2 + b2 = 458 ------- (i) a2 - b2 = 120 ------- (ii) By adding (i) and (ii), 2a2 = 578 a = ± 17 b = ± 13 We know, b > a and ab < 0. So, a = - 17 and b = 13 Thus, => a - b = - 17 - 13 = - 30Â
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