Question

9a^2 + 16b^2 + 25c^2 - 12ab -20bc - 15ac

a: b: c ??

Answer 1

3:4:5.

• An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.
• Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
• Algebraic identities are algebraic equations that hold true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Here, according to the given information, the expression is given as,

$9a^{2}+16b^{2} +25c^{2} -12ab-20bc-15ac$.

This expression can be written as,

$(3a)^{2} +(4b)^{2} +(5c)^{2} -2(3a.4b +4b.5c+5c.3a)\\=(3a+4b+5c)^{2}$

Hence, the coefficients of a, b and c, if taken into ratios, will be,

3:4:5.

Hence, the ratio of the coefficients is 3:4:5.

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