Question

If 5 + 2root3/7 + root3 = a-root3b find a and b where a and b are rational no

Answer 1

a = 29/46

b= - 9/46

Explanation:

Given:

• (5 + 2√3)/(7 + √3) = a - √3b

Rationalizing the left side:

• (5+2√3)(7-√3)/(7+√3)(7-√3) =
• (35 + 14√3 - 5√3 - 2√3²)/(7² - √3²) =
• (35 - 6 + 9√3)/(49 - 3) =
• (29 + 9√3)/46 =
• 29/46 + √3 (9/46)

Comparing the left and right sides:

• a - √3b = 29/46 + √3 9/46
• a = 29/46
• b = - 9/46