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3^2 x^2-7 x+7=9 | Numerade

Name: Problem 99, Chapter 7: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2021-07-29T16:44:25-08:00
Duration: 1 min 49 s
Channel: Anas Venkitta
Description: 3^2 x^2-7 x+7=9

Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax^2 + bx + c = 0. When solving problems that reduce to quadratic equations, methods such as factoring, completing the square, or using the quadratic formula can be applied to find the variable's possible values. This is a common occurrence in algebra where an equation initially involving exponents leads to a quadratic form after equating the exponents.

Exponential Equations

An exponential equation is one in which variables appear in the exponent. Solving these equations often involves rewriting the equation so that both sides have the same base, which then permits equating the exponents directly. This approach is a fundamental technique in algebra when dealing with growth, decay, or any process modelled by exponents.

Common Base Rewriting

Rewriting an expression to obtain a common base on both sides of an equation is crucial when working with exponential equations. For instance, recognizing that a number like 9 can be expressed as 3^2 allows one to set the equation in a unified exponential form, facilitating the application of exponent rules and reducing the problem to an algebraic equation on the exponents.

Equating Exponents

When an equation is expressed with the same base on both sides, the exponents can be equated directly. This method relies on the one-to-one property of exponential functions, which states that if the bases are equal and non-zero (and not equal to one), then the exponents must be equal. This technique simplifies the process of finding solutions in exponential equations.

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