Let = ⁻¹ ( 3 5 ) + ⁻¹ ( 5 13 ) and = ⁻¹ ( 3 5 ) + ⁻¹ ( 5 13 ) . The value of ( - ) is:

Step-by-step solution

Adding the expressions for and , we get: + = [ ⁻¹ ( 3 5 ) + ⁻¹ ( 3 5 ) ] + [ ⁻¹ ( 5 13 ) + ⁻¹ ( 5 13 ) ] Using the identity ⁻¹x + ⁻¹x = 2 , we have: + = 2 + 2 = = - We need to find ( - ) : ( - ) = ( - ( - )) = (2 - ) = ( - 2 ) = - (2 ) Now, we calculate : = ( ⁻¹ ( 3 5 ) + ⁻¹ ( 5 13 ) ) Using the formula (A + B) = A B + A B : = 3 5 1 - ( 5 13 )^2 + 5 13 1 - ( 3 5 )^2 = 3 5 12 13 + 5 13 4 5 = 36 65 + 20 65 = 56 65 Finally, we evaluate - (2 ) : - (2 ) = -(1 - 2 ^2 ) = 2 ^2 - 1 = 2 ( 56 65 )^2 - 1 = 2 ( 3136 4225 ) - 1