Question

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

Answer 1

Answer:

a:b = 2:1

Step-by-step explanation:

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

$=\frac{2+\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})}$

$=\frac{2+\sqrt{3}}{2^{2}-(\sqrt{3})^{2}}$

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

Therefore,

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

/* Compare both sides, we get

a = 2 , b = 1

Now ,

a:b = 2:1

•••♪

Answer 2

$\huge\sf{Answer:-}$

a + b √3 = 1/2 - √3

= 2 + √3/(2 - √3)(2+√3)

= 2 + √3/2²-√3²

= 2 + √3/4 - 3

= 2 + √3

So,

a + b √3 = 2 + √3

Hence,

• a = 2
• b = 1

So,

a:b = 2:1