Advertisements
Advertisements
Question
If \[\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y\sqrt{3}\] , then
Options
x = 13, y = −7
x = −13, y = 7
x = −13, y =- 7
x = 13, y = 7
Solution
Given that:`(5-sqrt3)/(2+sqrt3) = x+ysqrt3`We need to find x and y
We know that rationalization factor for `2+sqrt3` is`2-sqrt3` . We will multiply numerator and denominator of the given expression `(5-sqrt3)/(2+sqrt3)`by, 2-sqrt3` to get
`(5-sqrt3)/(2+sqrt3) xx (2-sqrt3)/(2-sqrt2) = (5 xx 2 - 5 xx sqrt3 - 2 xx sqrt3 +(sqrt3)^3)/((2)^2 - (sqrt3)^2)`
` (10-5sqrt3 - 2 sqrt3 +3)/((2)^2 -(sqrt3)^2)`
` = (13-7sqrt3) /(4-3)`
` = 13 - 7sqrt3.`
Since ` x + y sqrt3 = 13 - 7 sqrt3`
On equating rational and irrational terms, we get `x=13 and y= -7`
APPEARS IN
RELATED QUESTIONS
Simplify the following
`3(a^4b^3)^10xx5(a^2b^2)^3`
Prove that:
`(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)=abc`
Find the value of x in the following:
`5^(x-2)xx3^(2x-3)=135`
Find the value of x in the following:
`2^(x-7)xx5^(x-4)=1250`
If a and b are distinct primes such that `root3 (a^6b^-4)=a^xb^(2y),` find x and y.
Show that:
`((a+1/b)^mxx(a-1/b)^n)/((b+1/a)^mxx(b-1/a)^n)=(a/b)^(m+n)`
Write the value of \[\sqrt[3]{125 \times 27}\].
The value of x − yx-y when x = 2 and y = −2 is
If x-2 = 64, then x1/3+x0 =
If o <y <x, which statement must be true?
