Question

Solve : 4y2 +6/y2
=11. [Hint : Substitute x for y21
y?
​

Answer 1

Answer:

On solving   $4y^{2} +\frac{6}{y^{2} } = 11$  we get , value of   $y = \sqrt{\frac{3}{4} }$ or $y = \sqrt{2}$  .

Step-by-step explanation:

To solve : $4y^{2} +\frac{6}{y^{2} } = 11$

Given : substitute $x$ for $y^{2}$ .

Solution :

• Here, we will use the below following steps to find a solution using the transposition method:

1. We will Identify the variables and constants in the given equation.
2. Then we differentiate the equation as LHS and RHS.
3. We take constants at RHS leaving variable at LHS.
4. Simplify the equation using arithmetic operation as required to find the value of $x$ .
5. Then the result will be the solution for the given linear equation. By using the transposition method. we get,

•    $4y^{2} +\frac{6}{y^{2} } = 11$  
• Substituting value of $x$  for $y^{2}$ .  

       [tex]4x+\frac{6}{x } = 11 \\ \\\frac{4x^{2} + 6}{x} = 11 \\ \\4x^{2} + 6 = 11x \\ \\4x^{2} -11x +6 = 0\\ \\4x^{2} -8x-3x+6 = 0\\ \\4x (x-2) -3(x-2) = 0\\ \\(4x-3) (x-2) = 0\\ \\x= \frac{3}{4} , x = 2[/tex]  

• For , $y^{2} = x$  we have two values of $x$ .

         [tex]y^{2} =(\frac{3}{4} ) \\y = \sqrt{\frac{3}{4} } [/tex]     and  [tex]y^{2} =(2 )\\ y = \sqrt{2} [/tex]

Note :

Question for above solution is : solve   $4y^{2} +\frac{6}{y^{2} } = 11$  and find the value of $y$ . [Hint : Substitute $x$ for $y^{2}$]