Question

Solve the following for x: 3 x - 4/7+7/3x-4 =5/2

Answer 1

Answer:

$6 \: Or \: \frac{5}{2} \: are\\ \: two \: roots \:of \: given \: quadratic \: equation$

Step-by-step explanation:

$\frac{3x-4}{7}+\frac{7}{3x-4}=\frac{5}{2}$

$\implies \frac{(3x-4)^{2}+7^{2}}{(3x-4)7}=\frac{5}{2}$

$\implies \frac{(3x)^{2}+4^{2}-2\times 3x\times 4+49}{21x-28}=\frac{5}{2}$

$\implies \frac{9x^{2}+16-24x+49}{21x-28}=\frac{5}{2}$

$\implies 2(9x^{2}-24x+65)=5(21x-28)$

$\implies 18x^{2}-48x+130=105x-140$

$\implies 18x^{2}-48x+130-105x+140=0$

$\implies 18x^{2}-153x+270=0$

Divide each term by 9, we get

$\implies 2x^{2}-17x+30=0$

$\implies 2x^{2}-12x-5x+30=0$

$\implies 2x(x-6)-5(x-6)=0$

$\implies (x-6)(2x-5)=0$

$\implies x-6 =0 \: Or \: 2x-5=0$

$\implies x = 6 \: Or \: 2x=5$

$\implies x = 6 \: Or \: x=\frac{5}{2}$

Therefore,

$6 \: Or \: \frac{5}{2} \: are\\ \: two \: roots \:of \: given \: quadratic \: equation$

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Answer 2

Step-by-step explanation:

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