Question

Find m2+ 1 /m2 if m+ 1 /m = the square root of 71

Answer 1

Finding values

• Given. $m+\frac{m}=\sqrt{71}$

• To find. the value of $m^{2}+\frac{1}{m^{2}}$

Solution.

We know the algebraic formula,

$\quad\quad a^{2}+b^{2}=(a+b)^{2}-2ab$

Now, $m^{2}+\frac{1}{m^{2}}$

$\quad=(m+\frac{1}{m})^{2}-2(m)(\frac{1}{m})$

$\quad=(\sqrt{71})^{2}-2$

$\quad=71-2$

$\quad=69$

Answer. $m^{2}+\frac{1}{m^{2}}=69$

Note. To solve this type of problems, remember to check which algebraic identity formula is suitable under given conditions. Put the values and calculate; you will get your answer.