If a^{2}+b^{2}=45 and ab=18,find frac{1}{a}+f | vedclass

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(C) We need to find the value of $\frac{1}{a} + \frac{1}{b}$.First,simplify the expression: $\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}$.We know that

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(C) We need to find the value of $\frac{1}{a} + \frac{1}{b}$.First,simplify the expression: $\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}$.We know that $(a+b)^{2} = a^{2} + b^{2} + 2ab$.Substitute the given values: $(a+b)^{2} = 45 + 2(18) = 45 + 36 = 81$.Therefore,$a+b = \pm\sqrt{81} = \pm 9$.Now,substitute $a+b = \pm 9$ and $ab = 18$ into the expression $\frac{a+b}{ab}$:$\frac{a+b}{ab} = \frac{\pm 9}{18} = \pm \frac{1}{2}$.Since $\frac{1}{2}$ is one of the possible values and is provided in the options,the correct choice is $C$.

If $a^{2}+b^{2}=45$ and $ab=18$,find $\frac{1}{a}+\frac{1}{b}$.

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