Question

x^2 +1/x^2 = 27. find x+1/x

Answer 1

Answer:

± √29

Step-by-step explanation:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \bigg(x + \dfrac{x}{ {x}^{2} } \bigg) ^{2} = {x}^{2} + 2x \times \dfrac{1}{x} + \dfrac{1}{ {x}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \bigg(x + \dfrac{1}{x} \bigg) ^{2} = {x}^{2} + 2 + \dfrac{1}{ {x}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \bigg(x + \dfrac{1}{x} \bigg) = 27 + 2$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \bigg(x + \dfrac{1}{ {x}^{2} } \bigg) = 29$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: x + \dfrac{1}{x} = \pm \: \sqrt{27}$

polynomials :-

• polynomials : Polynomial are variable based dialect in the language of maths.

• In a common language , polynomials are defined as a string of variables and numbers put together.

• Highest power of a polynomial is called degree of polynomial.

• A constant polynomial is nothing but a monomial with degree zero.

• Equation: A condition or a constraint placed on x and y coordinates.

• Curve: A union of points that satisfy a particular condition.

• Remainder theorem: When p(x) is divided by (x - a) then the remainder is given by p(a).