Question

Find the positive value of Variable for which given. equation is satisfied. ​

Answer 1

Answer:

The positive value of the variables satisfying the equation:

i) 48

ii) does not exist

iii) 1

Step-by-step explanation:

i) Given

$\dfrac{x}{2}- \dfrac{x}{3} =8$

We can solve this by simplifying the given expression. First cross multiply the left hand side.

$\dfrac{3x-2x}{3\times 2} =8\\\implies \dfrac{x}{6} =8\\\implies x=8\times 6=48$

The positive value of which satisfies the given equation is 48.

ii)  Given

$\dfrac{7}{x}+35=\dfrac{1}{10}$

On cross multiplying the left hand side, we get,

$\dfrac{7+35x}{x} = \dfrac{1}{10} \\\\\implies 7+35x=\dfrac{x}{10}\\\implies 10(7+35x)=x\\\implies 70+350x=x\\\implies 350x-x=-70\\\implies 349x=-70\\\implies x=\dfrac{-70}{349}$

So, there does not exist a positive value for $x$ satisfying the given equation.

iii)  Given

$\dfrac{Y^2+4}{3Y^2+7}=\frac{1}{2}$

On simplifying the expression, we obtain

$3Y^2+7=2(Y^2+4)\\3Y^2+7=2Y^2+8\\3Y^2-2Y^2=8-7\\Y^2=1\\Y=\pm 1$

So, positive Y satisfying the equation is 1.