InterviewSolution
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InterviewSolution
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Prove that:(i) \({\sqrt\frac{1}{4}}=(0.01)^{-\frac{1}{2}}-(27)^{\frac{2}{3}}\) \(=\frac{3}{2}\)(ii) \(\frac{2^n+2^{n-1}}{2^{n+1}-2^n}\) \(=\frac{3}2\)(iii) \((\frac{64}{125})^{-\frac{2}{3}}\)\(+\frac{1}{(\frac{256}{625})^\frac{1}{4}}\)\(+(\frac{\sqrt{25}}{\sqrt[3]{64}})\) \(=\frac{65}{16}\)(iv) \(\frac{3^{-3}\times6^2\times\sqrt{98}}{5^2\times\sqrt[3]\frac{1}{25}\times(15){-\frac{4}{3}}\times3^{\frac{1}{3}}}\)(v) \(\frac{(0.6)^0-(0.1)^{-1}}{(\frac{3}{8})^{-1}(\frac{3}{2})^3+(-\frac{1}{3})^{-1}}\) \(=-\frac{3}{2}\) |
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Answer» (i) 1/2 + 1/(0.01) 1/2 -32 =1/2 + 10 – 9 =1/2 + 1 =3/2 (ii) (2 n + 2n-1)/ ) (2n+1 - 2n) =2 n(1 + 2-1 ) / 2n (2-1) = [1 + (1/2)]/1 =1 + 1/2 =3/2 (iii) (125/64) 2/3 + (625/256)1/4 + ( 5/4) =(5/4) 2 + 5/4 + 5/4 =25/16 + 5/4 + 5/4 =65/16 (iv) (3 -3.62.7(2)1/2)/ (54/3.(15)-4/3‑.31/3) =28(2)1/2 (3 -3.36.7(2)1/2)/ (54/3-4/3.(3)-1) (3 -2.36.7(2)1/2)/ (50) 1/9.36.7(2) 1/2 28\(\sqrt2\) (v) {1- 1/0.1}/ { (3/8) -1(3/2)3 + (-1/3)-1 =1-10/{ (8/3)(3/2) 3 + (-3) =-9/(3 2-3) = -3/2 |
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