if x=√5+2√3 / 7+√3 = a-b√3 find a and b where both are rational numbers
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Answer:
Given
(5 + 2√3) / (7 + √3) = a - b√3
By rationalization, we get
(5 + 2√3)(7 +√3) / (7 +4 √3) (7 - √3) = a - b√3
(35 - 5√3 + 14√3 – 6) /49-3= a - b√3
(29 + 9√3 ) /46= a -b√3
On equating the above equation, we get
a = 29/46 and b = -9/46
hope it helps
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