AP EAMCET · Maths · Basic of Mathematics
If \(\frac{a x+5}{\left(x^2+b\right)(x+3)}=\frac{x+21}{12\left(x^2+b\right)}+\frac{c}{12(x+3)}\), then \(b^2=\)
- A \(a^3-c\)
- B \(a^2+c\)
- C \(a-c\)
- D \(a+c\)
Answer & Solution
Correct Answer
(A) \(a^3-c\)
Step-by-step Solution
Detailed explanation
\(12(ax+5) = (x+21)(x+3) + c(x^2+b)\) \(12ax+60 = x^2+24x+63+cx^2+cb\) \(12ax+60 = (1+c)x^2+24x+(63+cb)\) Comparing coefficients: \(x^2: 0=1+c \implies c=-1\) \(x: 12a=24 \implies a=2\) \(Const: 60=63+cb \implies 60=63+(-1)b \implies b=3\) \(b^2 = 3^2 = 9\)…
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