CATAlgebra > Hard83+p+13q\dfrac{8}{3} + p + \dfrac{1}{3}q38+p+31q23−p+32q\dfrac{2}{3} - p + \dfrac{3}{2}q32−p+23q83−p+32q\dfrac{8}{3} - p + \dfrac{3}{2}q38−p+23q23−2p+23q\dfrac{2}{3} - 2p + \dfrac{2}{3}q32−2p+32q✅ Correct Option: 3Related questions:CAT 2024 Slot 2The roots α,β\alpha, \betaα,β of the equation 3x2+λx−1=03 x^{2}+\lambda x-1=03x2+λx−1=0, satisfy 1α2+1β2=15\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}=15α21+β21=15. The value of (α3+β3)2\left(\alpha^{3}+\beta^{3}\right)^{2}(α3+β3)2, isCAT 2020 Slot 2Let f(x)=x2+ax+bf(x)=x^{2}+a x+bf(x)=x2+ax+b and g(x)=f(x+1)−f(x−1)g(x)=f(x+1)-f(x-1)g(x)=f(x+1)−f(x−1). If f(x)≥0f(x) \geq 0f(x)≥0 for all real xxx, and g(20)=72g(20)=72g(20)=72, then the smallest possible value of bbb isCAT 2020 Slot 1The number of distinct real roots of the equation (x+1x)2−3(x+1x)+2=0(x + \frac{1}{x})^2 - 3(x + \frac{1}{x}) + 2 = 0(x+x1)2−3(x+x1)+2=0 equals