TS EAMCET · Maths · Quadratic Equation
If \(x=\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}\), then \(x^2(x-4)^2\) is equal to :
- A 7
- B 4
- C 2
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
\(\because \quad x=\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}=\sqrt{\frac{(2+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}}\) \(=\frac{2+\sqrt{3}}{\sqrt{4-3}}=2+\sqrt{3}\) \(\therefore x^2(x-4)^2=(2+\sqrt{3})^2(2+\sqrt{3}-4)^2\) \(=(\sqrt{3}+2)^2(\sqrt{3}-2)^2\)…
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
- If \(\cos \left(\frac{\pi}{4}-x\right) \cos 2 x+\sin x \sin 2 x \sec x\) \(=\cos x \sin 2 x \sec x+\cos \left(\frac{\pi}{4}+x\right) \cos 2 x\), then a possible value of sec \(x\) isTS EAMCET 2020 Medium
- A random variable \(\mathrm{X}\) has the following distribution. \begin{array}{|c|c|c|c|c|c|c|} \hline \boldsymbol{X}=\boldsymbol{x}_{\boldsymbol{i}} & -2 & -1 & 0 & 1 & 2 & 3 \ \hline \boldsymbol{P}\left(\boldsymbol{X}=\boldsymbol{x}_{\boldsymbol{i}}\right) & 0.1 & \mathrm{k} & 0.2 & 2 \mathrm{k} & 3 \mathrm{k} & \mathrm{k} \ \hline \end{array} Then the variance of this distribution isTS EAMCET 2023 Easy
- Consider the following statements Assertion (A) If \(P_1, P_2, P_3\) are probability of happening of three independent events, then probability of happening of atleast one of them is \(1-\left[\left(1-P_1\right)\left(1-P_2\right)\left(1-P_3\right)\right]\) Reason (R) For any three independent events \(A, B\) and \(C\) \(\begin{array}{r} P(A \cup B \cup C)=P(A)+P(B)+P(C)-P(A) P(B) \ -P(A) P(C)-P(B) P(C)+P(A) P(B) P(C) \end{array}\) The correct option among the following isTS EAMCET 2020 Easy
- The point where the line \(4 x-3 y+7=0\) touches the circle \(x^2+y^2-6 x+4 y-12=0\) isTS EAMCET 2016 Medium
- Consider the following statements Statement I If \(a_0+\frac{a_1}{2}+\frac{a_2}{3}+\ldots .+\frac{a_n}{n+1}=0\), where \(a_0, a_1, \ldots ., a_n\) are real numbers, then the polynomial \(a_0+a_1 x+a_2 x^2+\ldots .+a_n x^n\) has a zero in the interval \((0,1)\).Statement II If \(f:[a, b] \rightarrow \mathbf{R}\) is continuous on \([a, b]\) and \(f\) is differentiable in \((a, b)\), where \(a>0\) and if \(\frac{f(a)}{a}=\frac{f(b)}{b}\), then there exists \(c \in(a, b)\), such that \(c f^{\prime}(c)=f(c)\). Which one of the following options is true?TS EAMCET 2020 Easy
- In an acute angled triangle, \(\cot B \cot C+\cot A \cot C+\cot A \cot B\) is equal toTS EAMCET 2012 Easy
More PYQs from TS EAMCET
- A circular coil carrying a current of 2.5 A is free to rotate about an axis in its plane perpendicular to an external magnetic field. When the coil is made to oscillate, the time period of oscillation is T. If the current through the coil is 10 A , the time period of oscillation isTS EAMCET 2024 Easy
- For a first order reaction, the graph between \(\log \frac{a}{(a-x)}\) (on \(y\)-axis) and time (in min, on \(x\)-axis) gave a straight line passing through origin. The slope is \(2 \times 10^{-3} \mathrm{~min}^{-1}\). What is the rate constant (in \(\min ^{-1}\) )?TS EAMCET 2024 Medium
- At , a one litre solution of sucrose (molecular weight: ) was prepared by dissolving of sucrose. What is the approximate osmotic pressure (in ) of the solution at the same temperature?TS EAMCET 2018 Medium
- If the mean and variance of a binomial distribution are and respectively, thenTS EAMCET 2022 Medium
- If the points with position vectors \(\hat{i}-\hat{j}+\hat{k}, 2 \hat{i}-\hat{k}, \hat{j}+2 \hat{k}\) and \(\hat{i}+\hat{j}+\lambda \hat{k}\) are coplanar, then the magnitude of the vector \(6 \lambda \hat{i}-3 \hat{j}+6 \hat{k}\) isTS EAMCET 2023 Easy
- A message signal is used to modulate a carrier frequency. If the peak voltages of message signal and carrier signals are increased by \(0.1 \%\) and \(0.3 \%\) respectively, then the percentage change in modulation index isTS EAMCET 2019 Easy