Question

If a and b are rational numbers and a+b√3=1/2-√3,find a:b=?​

Answer 1

The value of the ratio a:b is 2:1

What is a surd?

Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.

Example of some surds are the square root of prime numbers.

Analysis:

a + b$\sqrt{3}$ = $\frac{1}{2 - \sqrt{3} }$

Rationalizing the right hand side by the conjugate surd which is 2 + $\sqrt{3}$

$\frac{1}{2 - \sqrt{3} }$  x $\frac{2 + \sqrt{3} }{2 +\sqrt{3} }$ = $\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}$ = $\frac{2 + \sqrt{3} }{1}$ = 2 + $\sqrt{3}$

Equating,

a + b$\sqrt{3}$ = 2 + $\sqrt{3}$

Comparing the variables,

a = 2,   b$\sqrt{3}$ = $\sqrt{3}$, b = 1

The ratio, a: b = 2:1

Learn more about surds: brainly.com/question/840021

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