Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Let $(a + b)^{Q (x)} + (a - b)^{Q (x) - 2 λ} = A$ Where $λ \in N, A \in R$ and $a^{2} - b = 1$ $∴ (a + b) (a - b) = 1 \Rightarrow (a + b) = (a - b)^{- 1}$ and $(a - b) = (a + b)^{- 1}$ i.e., $(a \pm b) = (a + b)^{\pm 1}$ or $(a - b)^{\pm 1}$

If $α, β$ are the roots of the equation $x^{2} - 4 x + 1 = 0$ , where $α > β$ , then the number of real solutions of the equation $α^{y^{2} - 2 y + 1} + β^{y^{2} - 2 y - 1} = \frac{101}{10 β}$ are

Options:

Answer:

Solution:

$x = 2 \pm 3$

$(2 + 3)^{y^{2 - 2 y + 1}} + (2 - 3)^{y^{2 - 2 y + 1}} = \frac{101}{10 ( 2 - 3 )} \Rightarrow (2 + 3)^{y^{2 - 2 y}} + (2 - 3)^{y^{2 - 2 y}} = \frac{101}{10}$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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