Question

Solve the sum with quadric equations .

Answer 1

♪Question:-

Solve the Equation:-

$\frac{x-1}{x+2}$+$\frac{x-3}{x-4}$=3$\frac{1}{3}$

→$\frac{x-1}{x+2}$+$\frac{x-3}{x-4}$=$\frac{10}{3}$

♦Answer:-

★Cross Multiplying LHS★

→$\frac{(x-1)(x-4)+(x+2)(x-3)}{(x+2)(x-4)}$=$\frac{10}{3}$

→$\frac{x^{2}-4x-x+4+x^{2}-3x+2x-6}{x^{2}-4x+2x-8}$=$\frac{10}{3}$

→$\frac{2x^{2}-6x-2}{x^{2}-2x-8}$$\frac{10}{3}$

★Cross Multiply LHS and RHS★

→6x²-18x-6=10x²-20x-80

→10x²-6x²-20x+18x-80+6

→4x²-2x-74

$\rule{200}{1}$

★Solving using Discriminant Formula★

→d=b²-4ac

a=4,b=(-2),c=(-74)

→(-2)²-4×4×(-74)

→4+1184

→1188=d

→√d=±√1188

→√d=±6√33

★Check Attachment for Factorization of √1188★

$\rule{200}{1}$

•Taking(+)=$\frac{-b+ \sqrt{d}}{2a}$

→x=$\frac{-(-2)+6 \sqrt{33}}{2×4}$

→x=$\frac{2+6 \sqrt{33}}{8}$

→x=$\frac{\cancel{2}(1+3 \sqrt{33}}{\cancel{8})}$

→x=$\frac{1+3 \sqrt{33})}{4}$

$\rule{200}{1}$

•Taking(-)=$\frac{-b- \sqrt{d}}{2a}$

→x=$\frac{-(-2)-6 \sqrt{33}}{2×4}$

→x=$\frac{2-6 \sqrt{33}}{8}$

→x=$\frac{\cancel{2}(1-3 \sqrt{33})}{\cancel{8}}$

→x=$\frac{1-3 \sqrt{33})}{4}$

$\rule{200}{8}$