Question

(ii) Solve : 4y2 +
6
- 11. [Hint : Substitute x for y?]
22.. wrong answer Krishna Gupta it's not 6 it's √2 and -√2is it's root​

Answer 1

Answer:

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "y2"   was replaced by   "y^2".  

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*y^2-(6)=0  

Step by step solution :

STEP

1

:

Equation at the end of step 1

 22y2 -  6  = 0  

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  4y2 - 6  =   2 • (2y2 - 3)  

Trying to factor as a Difference of Squares:

3.2      Factoring:  2y2 - 3  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

 

Check :  2  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step

3

:

 2 • (2y2 - 3)  = 0  

STEP

4

:

Equations which are never true:

4.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.2      Solve  :    2y2-3 = 0  

Add  3  to both sides of the equation :  

                     2y2 = 3

Divide both sides of the equation by 2:

                    y2 = 3/2 = 1.500

 

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     y  =  ± √ 3/2  

The equation has two real solutions  

These solutions are  y = ±√ 1.500 = ± 1.22474  

 

Two solutions were found :

y = ±√ 1.500 = ± 1.22474