If S = (sqrt{t^2 – 4t + 4}), find t in terms of S
-
A.
S2 – 2 -
B.
S + 2 -
C.
S – 2 -
D.
S2 + 2
Correct Answer: Option B
Explanation
S = (sqrt{t^2 – 4t + 4})
S2 = t2 – 4t + 4
t2 – 4t + 4 – S2 = 0
Using (t = frac{-b pm sqrt{b^2 – 4ac}}{2a})
Substituting, we have;
Using (t = frac{-(-4) pm sqrt{(-4)^2 – 4(1)(4 – S^2)}}{2(1)})
(t = frac{4 pm sqrt{16 – 4(4 – S^2)}}{2})
(t = frac{4 pm sqrt{16 – 16 + 4S^2}}{2})
(t = frac{4 pm sqrt{4S^2}}{2})
(t = frac{2(2 pm S)}{2})
Hence t = 2 + S or t = 2 – S
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