Question

If $(a+1/a-3)^2=16$ then find $a^3+1/a^3$

• A. 413
• B. 343
• C. 322
• D. 143

Answer 1

Answer:

C. 322

$(a+1/a-3)^2=16$

$a+1/a-3=\sqrt{16}=4$

$a+1/a-3=4$

$a+1/a=4+3=7$

$a^3+1/a^3=7^3-3\times7$

$=343-21$

$=322$

if $(a+1/a-3)^2=k$ then $a^3+1/a^3=k^3-3k$