Find the possible value or values of y in the quadratic equation 4 - 4y - y2 = 0.
Solution:
Quadratic equation 4 - 4y - y2 = 0
[Given]It can be written as- y2 - 4y + 4 = 0Using the quadratic formulay=−b±√b2−4ac2ay=−b±b2−4ac2aFrom the equation we know thata = - 1, b = - 4 and c = 4y=−(−4)±√(−4)2−4×−1×42×−1y=−(−4)±(−4)2−4×−1×42×−1By further calculationy=4±√16+16−2y=4±16+16−2y=4±4√2−2y=4±42−2Taking out 2 as commony=2(2±2√2)−2y=2(2±22)−2So we gety = - (2 ± 2√2)y = - (2 + 2√2) and y = - (2 - 2√2)y = - 2 - 2√2 and y = - 2 + 2√2Therefore, the possible values of y are - 2 - 2√2 and - 2 + 2√2.
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