Advertisements
Advertisements
प्रश्न
If \[x + \sqrt{15} = 4,\] then \[x + \frac{1}{x}\] =
विकल्प
2
4
8
1
उत्तर
Given that .`x+sqrt15 = 4` It can be simplified as
` x =4 -sqrt15`
`1/x = 1/(4-sqrt15)`
We need to find `x+1/x`
We know that rationalization factor for `4-sqrt15 `is `4 +sqrt15`. We will multiply numerator and denominator of the given expression `1/(4-sqrt15)`by , `4+sqrt15` to get
`1/x = 1/(4-sqrt15) xx (4+sqrt15)/ (4+sqrt15) `
`= (4+sqrt15)/((4^2) - (sqrt15)^2)`
`= (4+sqrt15)/(16-15)`
`= 4+sqrt15`
Therefore,
`x +1/x = 4 - sqrt15 + 4 + sqrt15`
` = 4+ 4 `
= ` 8 `
APPEARS IN
संबंधित प्रश्न
Simplify:
`((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)`
Show that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
Solve the following equation:
`3^(x+1)=27xx3^4`
State the quotient law of exponents.
The value of x − yx-y when x = 2 and y = −2 is
The product of the square root of x with the cube root of x is
The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is
If \[\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},\] then x =
The positive square root of \[7 + \sqrt{48}\] is
If \[\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =\]
