Question

if a is equal to √5+ √2÷ √5- √2 and b is equal to √5- √2÷ √5+ √2, show that 3a^2+4ab-3b^2 is equal to 4 +56/3 √ 10

Answer 1

a=(root5+root2)/(root5-root2)
b=(root5-root2)/(root5+root2)
ab=1
a+b=(root5+root2)^2+(root5-root2)^2 / (root5^2-root2^2)=2(root5^2+root2^2)/(5_2)
=2(5+2)/3=2×7/3
=14/3
a-b=4×root5×root2/3
=4root20/3
now 3(a^2_b^2)+4ab
=3×(14/3)×4root20/3=56root20/3



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