1. Using (a-b)3 = a3-b3-3ab(a-b), tick the correct expression:
A. X3+3x=p+(1/p) B.x3+3x=p-(1/p) C.x3+3x=p+1
2. If a = 31/4 + 3-1/4 and b=31/4 - 3-1/4 , then the value of (a2 + b2)2 is ………
3. If a = ( 21/2 + 1 )1/3 - (21/2 – 1)1/3 , then the value of a3 + 3a – 2 is ……….
4. On simplification ( ( xa/(a-b) / xa/(a+b) ) ÷ (xb/(b-a) / xb/(b+a)) ) a+b reduces to …………
1. b
2.20/3
3.a = 1
therefore,a^3+3a+-2
= 1+3-2
= 2
4. is a cyclical simplification so it reduces 1.
3. a + (2^0.5 -1 )^(1/3 ) = (2^0.5 +1)^(1/3) if we cube on both sides we get a^3 + 2^0.5 -1 +3*a*(2^0.5 -1 )^(1/3 )*(a + (2^0.5 -1 )^(1/3 )) = 2^0.5 + 1 implies a^3 + 2^0.5 -1 +3*a*(2^0.5 -1 )^(1/3 )*((2^0.5 +1)^(1/3)) = 2^0.5 + 1 implies a^3 +3a -2 = 0;
4. numerator:x^(a/(a-b) - a/(a+b)) = x^(2ab/(a^2-b^2))
similarly denominator is x^(2ab/(b^2 - a^2)) so total fraction is x^(4ab/(a^2-b^2)) so fraction power a+b is x^(4ab/(a-b))
2. a^2 = 3^0.5 +3^-0.5 +2 b^2 = 3^0.5 + 3^-0.5 -2 a^2 + b^2 = 2(3^0.5 + 3^-0.5) (a^2 + b^2)^2 = 4(3 + 1/3 + 2) = 64/3
CAclubindia
