Question

IF 5+ 2√3 / 7+4√3 = a+b√3, then find the value of a and b....

Answer 1

5+2√3/7+4√3
=5+2√3/7+4√3*(7-4√3/7-4√3)
=[(5+2√3)(7-4√3)] / 49-48
=5(7-4√3)+2√3(7-4√3)
=35-20√3+14√3-24
=11-6√3
=11+(-6)√3

Therfore, a=11 and b=(-6)

Answer 2

Answer:

a = 11 and b = -6

Step-by-step explanation:

Given,

$\frac{5+2\sqrt{3} }{7+4\sqrt{3} }$ = a+b$\sqrt{3}$

Solution:

$\frac{5+2\sqrt{3} }{7+4\sqrt{3} }$ = a+b$\sqrt{3}$

To rationalize the denominator, multiply and divide with a rationalizing factor

The rationalizing factor is 7 - 4$\sqrt{3}$

$\frac{5+2\sqrt{3} }{7+4\sqrt{3} }$  × $\frac{7 - 4\sqrt{3} }{7-4\sqrt{3} }$= a+b$\sqrt{3}$

$\frac{(5+2\sqrt{3})(7-4\sqrt{3})}{(7+4\sqrt{3}(7-4\sqrt{3})}$  = a+b$\sqrt{3}$

$\frac{35 -20\sqrt{3} +14\sqrt{3}-24 }{7^2 - (4\sqrt{3})^2}$ = a+b√3

11 - 6√3 = a+b√3

Comparing on both sides

a = 11 and b = -6

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