AP EAMCET · Maths · Functions
Solve the equation, \(3^{x^2-x}=25-4^{x^2-x}\)
- A -1 only
- B 2 only
- C Both -1 and 2
- D No solution
Answer & Solution
Correct Answer
(C) Both -1 and 2
Step-by-step Solution
Detailed explanation
Given equation \(3^{x^2-x}=25-4^{x^2-x}\) \(\Rightarrow \quad 4^{x^2-x}+3^{x^2-x}=25=4^2+3^2\) \(\begin{aligned} \Rightarrow & x^2-x=2 & \Rightarrow & x^2-x-2=0 \\ \Rightarrow & & (x-2)(x+1)=0 & \Rightarrow \quad x=-1,2 \end{aligned}\) Hence, option (c) is correct.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The value of ' \(k\) ' so that the line \(y=2 x+k\) may touch the ellipse \(3 x^2+5 y^2=15\) isAP EAMCET 2020 Easy
- The radius of the circle passing through the points of intersection of the circles \(x^2+y^2+2 x+4 y+1=0, x^2+y^2-2 x-4 y-4=0\) and intersecting the circle \(x^2+y^2=6\) orthogonally isAP EAMCET 2025 Hard
- \(\int\left(\frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}}\right) d x=\)AP EAMCET 2025 Medium
- A straight line \(L\) cuts both the lines \(5 x-y-4=0\) and \(3 x+4 y-4=0\). The segment of \(L\) between the two lines is bisected at the point \((1,5)\). The equation of \(L\) isAP EAMCET 2017 Medium
- Let \(\quad \overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \quad \overrightarrow{\mathbf{b}}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}} \quad\) and \(\overrightarrow{\mathbf{c}}=\lambda \hat{\mathbf{i}}+\hat{\mathbf{j}}+(2 \lambda-1) \hat{\mathbf{k}}\). If \(\overrightarrow{\mathbf{c}}\) is parallel to the plane containing \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}\), then \(\lambda\) is equal toAP EAMCET 2010 Medium
- If the bi-quadratic equation has as one of its roots, then which of the following is not a root ofAP EAMCET 2020 Easy
More PYQs from AP EAMCET
- The catalyst used for the isomerisation of n-alkanes to branched chain alkanes isAP EAMCET 2025 Easy
- Assertion (A) Order of the differential equations of a family of circles with constant radius is two.
Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.AP EAMCET 2022 Easy - If \(A\) is a square matrix of order 3 and \(A^2+A+2 I=0\), thenAP EAMCET 2018 Hard
- Higher second ionisation enthalpies than expected are observed forAP EAMCET 2022 Easy
- An analysis of monthly wages paid to the workers of two jute mills \(A\) and \(B\) gives the following data:
\begin{array}{lll}
No. of workers & Mill-A & Mill-B \\
Average daily wage (in rupees) & 500 & 600 \\
Variance of distribution of wages & 186 & 175 \\
81 & 100
\end{array}
ThenAP EAMCET 2023 Easy - If the energy gap of a substance is 5.4 eV , then the substance isAP EAMCET 2024 Easy