Find the value of a and b if 5+2√3/7+4√3 = a+b√3

Open in App

Solution

Lhs = (5+2√3)/(7+4√3)

= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]
=[35-20√3+14√3-24]/[7²-(4√3)²]
=[11-6√3]/[49-48]
=11-6√3
therefore
11-6√3 = a+b√3

compare both sides
a= 11, b= -6

Suggest Corrections

Similar questions

find the value of a and B if 5+2 √3 / 7+4√3 = A+B√3

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

a + b \sqrt{3}

Find the values of $a$ and $b$

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

Find the value of ' a ' and ' b ' if 5+2√3 / 7+4√3 = a+b√3

Join BYJU'S Learning Program