TS EAMCET · Maths · Quadratic Equation
\(\left(x^4+1\right)=\frac{1}{a}(x+1)^4\) is a reciprocal equation
- A only for a = 1
- B for all \(a \in \mathbb{R}-\{1\}\)
- C for all \(a \in \mathbb{R}\)
- D when \(a\) is an irrational number
Answer & Solution
Correct Answer
(B) for all \(a \in \mathbb{R}-\{1\}\)
Step-by-step Solution
Detailed explanation
Given equation is \(\left(x^4+1\right)=\frac{1}{a}(x+1)^4\) \[ \begin{aligned} & a\left(x^4+1\right)-(x+1)^4=0 \\ & a\left(x^4+1\right)-\left(x^4+4 x^3+6 x^2+4 x+1\right)=0 \\ & x^4(a-1)-4 x^3-6 x^2-4 x+(a-1)=0 \ldots \end{aligned} \] Compare the coefficients, Then,…
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