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QT - exponents or indices

rajiv (student) (197 Points)

25 May 2012

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 = 3^1/4 + 3^-1/4 and b=3^1/4- 3^-1/4, then the value of (a² + b²)² is ………

3. If a = ( 2^1/2 + 1 )^1/3 - (2^1/2 – 1)^1/3 , then the value of a³ + 3a – 2 is ……….

4. On simplification ( ( x^a/(a-b) / x^a/(a+b) ) ÷ (x^b/(b-a) / x^b/(b+a)) )^a+b reduces to …………

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3 Replies

intermediate(ipc)course (no) (1460 Points)
Replied 25 May 2012

1. b

2.20/3

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intermediate(ipc)course (no) (1460 Points)
Replied 25 May 2012

3.a = 1

therefore,a^3+3a+-2

= 1+3-2

= 2

4. is a cyclical simplification so it reduces 1.

Tejaswi Kasturi (student-cpt) (427 Points)
Replied 26 May 2012

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