Advertisements
Advertisements
प्रश्न
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
विकल्प
1
3
6
7
Advertisements
उत्तर
Given that: `x=2/(3+sqrt7)`
We know that rationalization factor for `3+sqrt7` is .`3-sqrt7` We will multiply numerator and denominator of the given expression `2/(3+sqrt7)` by `3 - sqrt7`, to get
`x = 2/(3+sqrt7) xx (3-sqrt7)/ (3-sqrt7)`
`= (2(3-sqrt7))/((3)^2 - (sqrt7)^2)`
`= (2(3-sqrt7))/(9-7) `
`= 3 - sqrt7`
Therefore,
`x-3 =-sqrt7`
On squaring both sides, we get
`(x-3)^2 = 7`
APPEARS IN
संबंधित प्रश्न
Simplify the following
`((4xx10^7)(6xx10^-5))/(8xx10^4)`
Prove that:
`1/(1 + x^(b - a) + x^(c - a)) + 1/(1 + x^(a - b) + x^(c - b)) + 1/(1 + x^(b - c) + x^(a - c)) = 1`
Solve the following equation for x:
`4^(2x)=1/32`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
Show that:
`(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)=1`
If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`
State the power law of exponents.
If \[\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y\sqrt{3}\] , then
The positive square root of \[7 + \sqrt{48}\] is
If \[x = \sqrt{6} + \sqrt{5}\],then \[x^2 + \frac{1}{x^2} - 2 =\]
