Question

Please find the value of x ​

Answer 1

Answer:

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Answer 2

Answer:

$\dfrac{x}{-\left(\dfrac{ap^4+bq^4}{q^2}\right)+b\left(p^2+q^2\right)}=\dfrac{1}{bq^2-ap^2}\quad :\quad x=\dfrac{p^2}{q^2};\quad \:q\ne \:0$

Step-by-step explanation:

$\dfrac{x}{-\left(\dfrac{ap^4+bq^4}{q^2}\right)+b\left(p^2+q^2\right)}=\dfrac{1}{bq^2-ap^2}$

$\gray{\mathrm{Multiply\:both\:sides\:by\:}bp^2q^2-ap^4}$

$\dfrac{x\left(bp^2q^2-ap^4\right)}{-\dfrac{ap^4+bq^4}{q^2}+b\left(p^2+q^2\right)}=\dfrac{1\cdot \left(bp^2q^2-ap^4\right)}{bq^2-ap^2}$

$\black{\mathrm{Simplify}}$

$\dfrac{x\left(bp^2q^2-ap^4\right)}{-\dfrac{ap^4+bq^4}{q^2}+b\left(p^2+q^2\right)}=\dfrac{1\cdot \left(bp^2q^2-ap^4\right)}{bq^2-ap^2}$

$\black{\mathrm{Simplify\:}\dfrac{x\left(bp^2q^2-ap^4\right)}{-\dfrac{ap^4+bq^4}{q^2}+b\left(p^2+q^2\right)}}$

$\dfrac{x\left(bp^2q^2-ap^4\right)}{-\dfrac{ap^4+bq^4}{q^2}+b\left(p^2+q^2\right)}$

$\gray{\mathrm{Join}\:-\dfrac{ap^4+bq^4}{q^2}+b\left(p^2+q^2\right):\quad \dfrac{bp^2q^2-ap^4}{q^2}}$

$=\dfrac{x\left(-ap^4+bp^2q^2\right)}{\dfrac{bp^2q^2-ap^4}{q^2}}$

$\gray{\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{a}{\dfrac{b}{c}}=\dfrac{a\cdot \:c}{b}}$

$=\dfrac{x\left(bp^2q^2-ap^4\right)q^2}{bp^2q^2-ap^4}$

$\gray{\mathrm{Cancel\:the\:common\:factor:}\:bp^2q^2-ap^4}$

$=xq^2$

$\black{\mathrm{Simplify\:}\dfrac{1\cdot \left(bp^2q^2-ap^4\right)}{bq^2-ap^2}}$

$\dfrac{1\cdot \left(bp^2q^2-ap^4\right)}{bq^2-ap^2}$

$\gray{1\cdot \left(bp^2q^2-ap^4\right)=bp^2q^2-ap^4}$

$=\dfrac{bp^2q^2-ap^4}{bq^2-ap^2}$

$\gray{\mathrm{Factor}\:bp^2q^2-ap^4:\quad p^2\left(bq^2-ap^2\right)}$

$=\dfrac{p^2\left(bq^2-ap^2\right)}{bq^2-ap^2}$

$\gray{\mathrm{Cancel\:the\:common\:factor:}\:bq^2-ap^2}$

$=p^2$

$xq^2=p^2$

$\gray{\mathrm{Divide\:both\:sides\:by\:}q^2;\quad \:q\ne \:0}$

$\dfrac{xq^2}{q^2}=\dfrac{p^2}{q^2};\quad \:q\ne \:0$

$\gray{\mathrm{Simplify}}$

$x=\dfrac{p^2}{q^2};\quad \:q\ne \:0$

$\blue{\mathrm{Plotting:}}$

$\dfrac{x}{-\left(\dfrac{ap^4+bq^4}{q^2}\right)+b\left(p^2+q^2\right)}=\dfrac{1}{bq^2-ap^2}\quad \mathrm{assuming}\quad \:a=1\quad \:p=2\quad \:b=3\quad \:q=4$