1) 25x-1 = 22x-1 100 , find x 2) X = 21/3 + 22/3 , show that x3 - Maths - Number Systems

Question

1) 25x-1 = 22x-1 – 100 , find x
2) X = 21/3 + 22/3 , show that
x3 – 6x = 6
3)   Find - – 6x = 6
4) Find - √ 42 × 34 ×
(cube – root3-3 ) √5-2 ÷
6th root 312 × 5-6
5) If ax = by =cz and
b2 = ac , then show that y = 2zx ÷ z + x
6) If x = 6 - √35 , find x3 + 1 /
x3
please answer fast

Lalit Mehra · Accepted Answer

6 $x = 6 - \sqrt{35} ∴ \frac{1}{x} = \frac{1}{6 - \sqrt{35}} \times \frac{6 + \sqrt{35}}{6 + \sqrt{35}} = \frac{6 + \sqrt{35}}{36 - 35} = 6 + \sqrt{35} x^{3} + \frac{1}{x^{3}} = (6 - \sqrt{35})^{3} + {(6 + \sqrt{35})}^{3} = 2 \times (6)^{3} + 2 \times 3 \times 6 \times (\sqrt{35})^{2} = 2 \times 216 + 36 \times 35 = 1692$ 5 ax = by = cz = k â‡’ ax = k , by = k , cz = k $\Rightarrow a = k^{\frac{1}{x}}, b = k^{\frac{1}{y}}, c = k^{\frac{1}{z}} G i v e n, b^{2} = a c ∴ (k^{\frac{1}{y}})^{2} = k^{\frac{1}{x}} \times k^{\frac{1}{z}} \Rightarrow k^{\frac{2}{y}} = k^{\frac{1}{x} + \frac{1}{z}} \Rightarrow \frac{2}{y} = \frac{1}{x} + \frac{1}{z} \Rightarrow \frac{2}{y} = \frac{x + z}{x z} \Rightarrow y = \frac{2 x z}{x + z}$ We are happy to see the interest you are showing towards this section! Thank you for your response I have already posted the answer to your two questions However, due to a paucity of time we will not be able to immediately answer all your queries Try to solve the remaining question If you have any problem in solving the question, then get back to us We will be happy to help you

1) 25x-1 = 22x-1 – 100 , find x 2) X = 21/3 + 22/3 , show that x3 – 6x = 6 3) Find - – 6x = 6 4) Find - √ 42 × 34 × (cube – root3-3 ) √5-2 ÷ 6th root 312 × 5-6 5) If ax = by =cz and b2 = ac , then show that y = 2zx ÷ z + x 6) If x = 6 - √35 , find x3 + 1 / x3 please answer fast