Question

if a ^2 - 3a +1 =0 and a is not equal to 0 find a+1/a​

Answer 1

GIVEN :-

• $\rm{a^2-3a+1 =0}$.

• a is not equal to zero.

TO FIND :-

• Find the value of $\rm{a+\dfrac{1}{a}}$.

Now,

$\implies\rm{a^2-3a+1 = 0}$

$\implies\rm{a^2-3a = -1}$

$\implies\rm{a(a-3) = -1}$

$\implies\rm{a-3 = \dfrac{-1}{a}}$

$\implies\rm{a - 3 +\dfrac{1}{a} = 0}$

$\implies\rm{a +\dfrac{1}{a} = 3}$.

Hence, The value of a +1/a is 3.

SOME IDENTITIES

$\boxed{\begin{minipage}{7cm}\\ \\ \sf\bf{(a+b)^2= \tt a^2+2ab+b^2 }\\ \\ \tt\bf{(a-b)^2= \tt a^2-2ab+b^2 }\\ \\ \rm\bf{a^3+b^3= \tt (a+b) (a^2-ab+b^2) }\\ \\ \rm\bf{a^3-b^3 = \tt (a-b) (a^2+ab+b^2) }\\ \\ \rm\bf {(a+b+c)^2 = \tt a^2+b^2+c^2+2ab+2bc+2ac }\end{minipage}}$

Answer 2

Given :-

• $\rm \: a {}^{2} - 3a \: + 1 = 0$
• $\rm \: a ≠ 0$

To Find :-

• $\rm \: Calculate \: \: the \: \: value \: \: of \: \: a \: + \: \frac{1}{a} .$

Solution :-

$\rm \implies \: a {}^{2} - 3a + 1 = 0$

$\rm \implies a(a - 3) + 1 = 0$

$\rm \implies a (a - 3) = - 1$

$\rm \implies a - 3 = \frac{ -1 }{a}$

$\rm \implies a \: - 3 + \frac{1}{a} = 0$

$\rm \implies \red{ \rm{a \: + \frac{1}{a} = 3 }}$

$\rm \: \bold { \underline{Thus, \: \: the \: \: value \: \: of \: \: a + \frac{1}{a} \: \: is \: \: 3.}}$