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प्रश्न
Solve the following equation by using formula :
4x2 – 4ax + (a2 – b2) = 0
उत्तर
4x2 – 4ax + (a2 – b2) = 0
Here a = 4, b = -4a, c = a2 - b2
D = b2 - 4ac
= (-4a)2 - 4 x 4(a2 - b2)
= 16a2 - 16(a2 - b2)
= 16a2 - 16a2 + 16b2
D = 16b2
∵ x = `(-b ± sqrt("D"))/(2a)`
= `(-(-4a) ± sqrt(16b^2))/(2 xx 4)`
= `(4a ± 4b)/(8)`
= `(a + b)/(2)`
∴ `x_1 = (a + b)/(2), x_2 = (a - b)/(2)`
Hence x = `(a + b)/(2), (a - b)/(2)`.
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