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Question
Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x
Solution
f(x) = `sqrt(x) - 3`, g(x) = 5 – x
f(x) = g(x)
∴ `sqrt(x) - 3` = 5 – x
∴ `sqrt(x)` = 5 – x + 3
∴ `sqrt(x)` = 8 – x
On squaring, we get
∴ `(sqrt(x))^2 = ( 8 – x)^2` ...[∴ (a − b)2 = a2 − 2ab + b2]
x = 64 – 16x + x2
∴ 64 – 16x – x + x2 = 0
∴ x2 – 17x + 64 = 0
Factorize or use the quadratic formula:
x = `(-b ± sqrt(b^2 - 4ac))/(2a)`
where a = 1, b = –17, and c = 64
x = `(-(-17) ± sqrt((-17)^2 - 4(64)))/2`
= `(17 ± sqrt(289 - 256))/2`
= `(17 ± sqrt(33))/2`
∴ x = `(17 + sqrt(33))/2` or x = `(17 - sqrt(33))/2`
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