यदि (f(x)=x) और (g(x)=x+1) हैं, तो ((f+g)(x)=(fg)(x)) के सही हल चुनिए।
If (f(x)=x) and (g(x)=x+1), choose the correct solutions of ((f+g)(x)=(fg)(x)).
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{1+\sqrt{5}}{2},\frac{1-\sqrt{5}}{2}\)
Concept
((f+g)(x)=2x+1) and ((fg)(x)=x(x+1)), so \(x^2-x-1=0\). The quadratic formula gives \(\frac{1\pm\sqrt{5}}{2}\).
Why this answer is correct
The correct answer is A. \(x=\frac{1+\sqrt{5}}{2},\frac{1-\sqrt{5}}{2}\). ((f+g)(x)=2x+1) and ((fg)(x)=x(x+1)), so \(x^2-x-1=0\). The quadratic formula gives \(\frac{1\pm\sqrt{5}}{2}\).
Exam Tip
((f+g)(x)=2x+1) और ((fg)(x)=x(x+1)), इसलिए \(x^2-x-1=0\)। द्विघात सूत्र से सही हल \(\frac{1\pm\sqrt{5}}{2}\) हैं।
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