Question

Solve the following quadratic equations by factorization:
7x+3/x=35 (3/5)

Answer 1

Step-by-step explanation:

therefore

7x-3/5=0

7x=3/5

x=3/35

therefore x=3/35

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Answer 2

SOLUTION :-

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:We\: have,\:7x+\bf\dfrac{3}{x}\:=\:35\bf\dfrac{3}{5}$

$\:$

$\:\:\:\:\:\:\:\:\:────────────────────$

$\:$

${\large{\frak{\pmb{\underline{Now, }}}}}$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \mapsto \:\bf\dfrac{7x²+3}{x}\:=\:35+\bf\dfrac{3}{5}$

$\:\:$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mapsto\:7x²+3\:=\:\bigg(35+\bf\dfrac{3}{5}\bigg)x$

$\:\:$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\mapsto\:7x²-\bigg( 35 + \bf\dfrac{3}{5}\bigg)x+3\:=\:0$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:|split\:the\:mid.\:term|$

$\:\:$

$\sf \:\:\:\:\:\:\:\:\:\:\dashrightarrow\:7x²\:-\:35x\:-\:\bf\dfrac{3}{5}x\:+\:3\:=\:0$

$\:\:$

$\sf \:\:\:\:\leadsto\:7x²\:-\:35x\:-\:\bf\dfrac{1}{5}(3x-3×5)\:=\:0$

$\:\:$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\leadsto7x(x-5)\:-\:\bf\dfrac{3}{5}(x-5)\:=\:0$

$\:\:$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\leadsto(x-5)\bigg( 7x -\bf\dfrac{3}{5}\bigg)\:=\:0$

$\:\:$

$\:$

$\sf \implies(x-5)\:=\:0\:\:\:\:\:\:\:\:or\:\:\:\:\:\:\:\:\:7x-\bf\dfrac{3}{5}\:=\:0$

$\:\:$

$\sf \small\bf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\underline {\mathcal{\purple{ x\:=\:\bf5}}}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:or\:\:\:\:\:\:\:\:\:\:\:\:\:$$\small{\underline{\mathcal{\red{ x\:=\:\bf\dfrac{3}{35}}}}}$