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17. Solve the following equation for x:9x2-9(p + q)x + (2p2 + 5pq + 2f)-0 |
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Answer» Consider, 9x^2-9(a+b)x+(2a^2+5ab+2b^2)=0 9x^2- 9(a + b)x + (2a^2+ 4ab + ab + 2b^2) = 0 9x^2- 9(a + b)x + [2a(a + 2b) + b(a + 2b)] = 0 9x^2- 9(a + b)x + [(a + 2b)(2a + b)] = 0 9x^2– 3[(a + 2b) + (2a + b)]x + [(a + 2b)(2a + b)] = 0 9x^2– 3(a + 2b)x - 3(2a + b)x + [(a + 2b)(2a + b)] = 0 3x[3x – (a + 2b)] - (2a + b)[3x + (a – 2b)] = 0 [3x – (a + 2b)][3x - (2a + b)] = 0 [3x – (a + 2b)] = 0 or [3x - (2a + b)] = 0 3x = (a + 2b) or 3x = (2a + b)x = (a + 2b)/3 or x = (2a + b)/3 |
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