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प्रश्न
If \[\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y\sqrt{3}\] , then
विकल्प
x = 13, y = −7
x = −13, y = 7
x = −13, y =- 7
x = 13, y = 7
उत्तर
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`
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