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If x + 1/x = 5, find the value of x2 + 1/x2.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The value of x2 + 1/x2, if x + 1/x = 5 is 23. Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Now we have to compute the required value.
Given that,
x + 1/x = 5
On squaring both sides, we get;
(x + 1/x)2 = 25
As we know that (a + b)2 = a2 + b2 + 2ab
x2 + 1/x2 + 2 = 25
On simplifying we get
x2 + 1/x2 = 23
Table of content
Algebraic Identities
Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. In order to compute algebraic expressions and solve various polynomials, algebraic identities are applied in this manner.
An expression with variables and constants is said to be algebraic. Variables in expressions can have any value. As a result, if the values of the variables change, the expression’s value may also change. However, algebraic identity is equality that holds true regardless of the variable’s value.
Summary:
If x + 1/x = 5, find the value of x2 + 1/x2.
The value of x2 + 1/x2, if x + 1/x = 5 is 23. Algebraic identities are equations in algebra that are true no matter what each variable’s value is. They are additionally used in the factorization of polynomials.
