Maths-
General
Easy
Question
Find the value of 𝑚 & 𝑛 to make a true statement.
(𝑚𝑥 + 𝑛𝑦)2 = 4𝑥2 + 12𝑥𝑦 + 9𝑦2
Hint:
The methods used to find the product of binomials are called special products.
Multiplying a number by itself is often called squaring.
For example (x + 3)(x + 3) = (x + 3)2
The correct answer is: (2,2) and (-2,-2).
(mx + ny)2 can be written as (mx + ny)(mx + ny)
(mx + ny)(mx + ny) = mx(mx + ny) + ny(mx + ny)
= mx(mx) + mx(ny) + ny(mx) + ny(ny)
= m2x2 + mnxy + mnxy + n2y2
= m2x2 + 2mnxy + n2y2
Now, m2x2 + 2mnxy + n2y2 = 4𝑥2 + 12𝑥𝑦 + 9𝑦2
Comparing both sides, we get
m2 = 4, n = 9, 2mn = 12
So, m = +2 or -2 , n = +3 or -3
Considering 2mn = 12, there are two combinations possible
- m = +2 and n = +2
- m = -2 and n = -2
Final Answer:
Hence, the values of (m, n) are (2,2) and (-2,-2).
Related Questions to study
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A symbol (usually a letter) in algebra represents an unknown numerical value in an algebraic expression or an equation. A variable is a non-fixed quantity that can be changed. Variables are essential because they are a significant component of algebra.
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points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
i)Which equation models the scoring in the final round and the outcome of the contest
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¶ Different Types of Variables
¶Dependent Variables: The variables whose values are determined by another variable's quantity.
¶Unrelated Variables: The values of an independent variable in an algebraic equation are unaffected by changes. Suppose an algebraic equation has two variables, x and y, and each x value is related to any other y value. In that case, x is an independent variable, and y is a dependent variable.
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