If both a and b are rational numbers, find the values of a and b in each of the given equality: root2+ root3 / 3 root2 −2 root3 = a – b root6
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√2+√3/3√2-2√3=a-b√6
LHS=√2+√3/3√2-2√3
=√2+√3/3√2-2√3×3√2+2√3/3√2+2√3
=(√2+√3)(3√2+2√3)/(3√2)² - (2√3)²
=√2(3√2+2√3)+√3(3√2+2√3)/9×2 - 4×3
=3×2+2√6+3√6+2×3/18-12
=6+5√6+6/6
=6+6+5√6/6
=12+5√6/6
after comparing
a=12/6=2
b=-5/6
thus, √2+√3/3√2-2√3=2-5/6√6
LHS=√2+√3/3√2-2√3
=√2+√3/3√2-2√3×3√2+2√3/3√2+2√3
=(√2+√3)(3√2+2√3)/(3√2)² - (2√3)²
=√2(3√2+2√3)+√3(3√2+2√3)/9×2 - 4×3
=3×2+2√6+3√6+2×3/18-12
=6+5√6+6/6
=6+6+5√6/6
=12+5√6/6
after comparing
a=12/6=2
b=-5/6
thus, √2+√3/3√2-2√3=2-5/6√6
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