Question

if m² – 3m – 1 = 0, find the value of m²+1/m²​
​

Answer 1

ᎯᏁᏕᏯᎬᏒ = 7

$\large{ \underline{ \underline{ \text{ \gray{✤Given}}}}}$

$\sf{ {m}^{2} - 3m - 1 = 0}$

$\sf{ = > {m}^{2} - 1 = 3m}$

$\sf{ = > m - \frac{1}{m} = 3} \: \: \mathcal{ \blue{ \boxed{Dividing \: both \: sides \: by \: m}}}$

$\large{ \text{ \red{Now;}}}$

$\sf{ {m}^{2} + \frac{1}{m {}^{2} } }$

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

$\sf{ = (m - \frac{1}{m} ) {}^{2} - 2 \times m \times \frac{1}{m} }$

$\sf{ = (3) {}^{2} - 2}$

$\sf{ \orange{ \boxed{ = 7}}}$

$\underline{\green{ \mathcal{Ꮋence \: m + \frac{1}{m} = 7}}}$

Important Formulas :

$\large{ \bold{ \sf{1.{a}^{2} + b {}^{2} }} = (a + b) {}^{2} - 2ab}$

$\large{ \bold{ \sf{2.a {}^{2} + b {}^{2} }} = (a - b) {}^{2} + 2ab}$

ᎻᎾᏢᎬ ᎿᎻᎨᏕ ᎻᎬᏝᏢᏕ ᎽᎾᏬ!!

Answer 2

Answer:

m + 1/m = 7

ʜᴏᴘᴇ ʏᴏᴜ ᴀʀᴇ sᴀᴛɪsғɪᴇᴅ ᴡɪᴛʜ ᴛʜᴀᴛ ᴀɴsᴡᴇʀ⬆