please help me in this and please tell with solution
Answers
\frac{3x-4}{7}+\frac{7}{3x-4}=\frac{5}{2}73x−4+3x−47=25
\implies \frac{(3x-4)^{2}+7^{2}}{(3x-4)7}=\frac{5}{2}⟹(3x−4)7(3x−4)2+72=25
\implies \frac{(3x)^{2}+4^{2}-2\times 3x\times 4+49}{21x-28}=\frac{5}{2}⟹21x−28(3x)2+42−2×3x×4+49=25
\implies \frac{9x^{2}+16-24x+49}{21x-28}=\frac{5}{2}⟹21x−289x2+16−24x+49=25
\implies 2(9x^{2}-24x+65)=5(21x-28)⟹2(9x2−24x+65)=5(21x−28)
\implies 18x^{2}-48x+130=105x-140⟹18x2−48x+130=105x−140
\implies 18x^{2}-48x+130-105x+140=0⟹18x2−48x+130−105x+140=0
\implies 18x^{2}-153x+270=0⟹18x2−153x+270=0
Divide each term by 9, we get
\implies 2x^{2}-17x+30=0⟹2x2−17x+30=0
\implies 2x^{2}-12x-5x+30=0⟹2x2−12x−5x+30=0
\implies 2x(x-6)-5(x-6)=0⟹2x(x−6)−5(x−6)=0
\implies (x-6)(2x-5)=0⟹(x−6)(2x−5)=0
\implies x-6 =0 \: Or \: 2x-5=0⟹x−6=0Or2x−5=0
\implies x = 6 \: Or \: 2x=5⟹x=6Or2x=5
\implies x = 6 \: Or \: x=\frac{5}{2}⟹x=6Orx=25
Therefore,
\begin{gathered} 6 \: Or \: \frac{5}{2} \: are\\ \: two \: roots \:of \: given \: quadratic \: equation \end{gathered}6Or25aretworootsofgivenquadraticequation
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Answer:
7x+4+3x-5
7x+3x+4-5
10x-1