Question

Find the root of the following equation

step by step explanation


if don't know no need to answer​

Answer 1

Step-by-step explanation:

I am sorry if I had done any mistake, I have shown all steps in the above paper

Answer 2

We're given,

$\longrightarrow \sf{\dfrac{1}{x + 4} - \dfrac{1}{x - 7} = \dfrac{11}{30}}$

$\longrightarrow \sf{\dfrac{(x-7) - (x + 4)}{(x+4)(x-7)} = \dfrac{11}{30} }$

$\longrightarrow \sf{\dfrac{x - 7 - x - 4 }{ {x}^{2} - 7x + 4x - 28} = \dfrac{11}{30} }$

$\longrightarrow \sf{\dfrac{-\cancel{11}}{ {x}^{2} - 3x - 28} = \dfrac{\cancel{11}}{30} }$

$\longrightarrow \sf{\dfrac{-1}{ {x}^{2} - 3x - 28} = \dfrac{1}{30} }$

$\longrightarrow \sf{1( {x}^{2} - 3x - 28) = -1(30) }$

$\longrightarrow \sf{ {x}^{2} - 3x + 2 = -30}$

$\longrightarrow \sf{ 0 = {x}^{2} - 3x + 2}$

$\longrightarrow \sf{ 0 = {x}^{2} - 2x - x + 2 }$

$\longrightarrow \sf{ x(x - 2) -1(x - 2) = 0}$

$\longrightarrow \sf{ (x - 2)(x - 1) = 0}$

$\sf{\\}$

Hence roots are,

$\longrightarrow \underline{\underline{\sf{x = 1\: or\: x = 2}}}$