Solve the equation frac{p + q - x}{r} + frac{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the equation: $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{4x}{p + q + r} = 0$.Add $1$ to each of the first thre

Vedclass · Accepted Answer

$x = p + q + r$

Vedclass · Answer

(A) Given the equation: $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{4x}{p + q + r} = 0$.Add $1$ to each of the first three terms to simplify:$(\frac{p + q - x}{r} + 1) + (\frac{q + r - x}{p} + 1) + (\frac{r + p - x}{q} + 1) + \frac{4x}{p + q + r} - 3 = 0$$\frac{p + q + r - x}{r} + \frac{q + r + p - x}{p} + \frac{r + p + q - x}{q} + \frac{4x - 3(p + q + r)}{p + q + r} = 0$$(p + q + r - x) (\frac{1}{r} + \frac{1}{p} + \frac{1}{q}) + \frac{4x - 3(p + q + r)}{p + q + r} = 0$Alternatively,rewrite the equation as:$(\frac{p + q - x}{r} + 1) + (\frac{q + r - x}{p} + 1) + (\frac{r + p - x}{q} + 1) + \frac{4x}{p + q + r} - 3 = 0$$(p + q + r - x) (\frac{1}{p} + \frac{1}{q} + \frac{1}{r}) = 3 - \frac{4x}{p + q + r}$$(p + q + r - x) (\frac{1}{p} + \frac{1}{q} + \frac{1}{r}) = \frac{3(p + q + r) - 4x}{p + q + r}$Setting $(p + q + r - x) = 0$ gives $x = p + q + r$.

Solve the equation $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{4x}{p + q + r} = 0$.

Similar Questions

If the roots of the given equation $(\cos p-1) x^2+(\cos p) x+\sin p=0$ are real,then

If one root of the equation $x(x + 2) = 3 - ax^2$ approaches infinity,then the value of $a$ approaches which of the following?

The roots of the quadratic equation $x^2 - 2\sqrt{3}x - 22 = 0$ are:

If the roots of the equation $ax^2 + x + b = 0$ are real and distinct,then what will be the nature of the roots of the equation $x^2 - 4\sqrt{ab}x + 1 = 0$?

If $A$ and $G$ represent the arithmetic mean and geometric mean respectively,and $x^2 - 2Ax + G^2 = 0$,then which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module