Question

Q 1- Find the products ( x - 1 ) ( x + 1 ) ( X2+ 1 ) ( X4+ 1 ) Q 2 - evaluate by using identity ( 0 . 99 )2 Q 3 - if X + 1X= 6 , find X4+ 1X4 Q 4- if x2+ 1x2= 27 , Find the value of x - 1x Q 5 - prove that 2a2+ 2 b2+ 2 c2- 2ab - 2bc - 2ca = [ ( a - b )2+ ( b - c)2+ ( c - a )2] Q 6 - if a2+ b2+ c2- ab - bc -ca = 0 , prove that a = b = c Q 7 - Simplify ( a + b + c )2+ ( a - b- c )2 Q 8- if a2+ b2+ c2= 20 and a + b + c = 0 , find ab + bc + ca Q 9 - if a + b + c = 9 and ab + bc + ca= 40 , find a2+ b2+ c2. Q 10 - write in expanded form ( 14a - 12b + 1 )2

Answer 1

Answer:

Step-by-step explanation:

using the identity (a+b)(a-b) =a²- b² in all cases

   [x+1/x][x-1/x][x²+1/x²][x⁴+1/x⁴]

= [x²- 1/x²][x²+1/x²][x⁴+1/x⁴]

=[(x²)²- (1/x²)²][x⁴+1/x⁴]

=[x⁴- 1/x⁴][x+1/x⁴]

=(x⁴)² - (1/x⁴)²

=x⁸-1/x⁸