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(((625)-½)-¼)2.

Consider the given expression. \(\begin{array}{l}\left(\left((625)^{-1 / 2}\right)^{-1 / 4}\right)^{2} \Rightarrow(625)^{\frac{-1}{2} \times \frac{-1}{4} \times 2} \\ \Rightarrow(625)^{\frac{1}{4}} \\ \Rightarrow \sqrt[4]{625} \\... View Article

If x2 + y2 + (1 / x2) + (1 / y2) = 4, then the value of x2 + y2 is

Consider the given function. \(\begin{array}{l}\mathrm{x}^{2}+\mathrm{y}^{2}+\frac{1}{\mathrm{x}^{2}}+\frac{1}{\mathrm{y}^{2}}=4\\ \Rightarrow x^{2}+y^{2}+\frac{1}{x^{2}}+\frac{1}{y^{2}}-4=0\\ \mathrm{x}^{2}+\frac{1}{\mathrm{x}^{2}}+\mathrm{y}^{2}+\frac{1}{\mathrm{y}^{2}}-2-2=0\\ \Rightarrow\left(\mathrm{x}^{2}+\frac{1}{\mathrm{x}^{2}}-2\right)+\left(\mathrm{y}^{2}+\frac{1}{\mathrm{y}^{2}}-2\right)=0\\ \left(x-\frac{1}{x}\right)^{2}+\left(y-\frac{1}{y}\right)^{2}=0\\ \Rightarrow\left(x-\frac{1}{x}\right)=0 \&\left(y-\frac{1}{y}\right)=0 \quad\left(\text { Since }\left(x-\frac{1}{x}\right)^{2} \&\left(y-\frac{1}{y}\right)^{2}\right.\\ \text { (both... View Article

If 3x – 3x-1 = 18, then xx =

The given expression is \(\begin{array}{l}3^{\mathrm{x}}-3^{\mathrm{x}-1}=18 \\ \Rightarrow 3^{x}-\frac{3^{x}}{3}=18 \\ \Rightarrow 3^{x}\left(\frac{2}{3}\right)=18 \\ 3^{\mathrm{x}-1} \cdot 2=3^{2} \cdot 2 \\ \quad \mathbf{x}-1=\mathbf{2}... View Article