Question

Find whether the equations x2 – 4x + 1.5 = 0 and 2x2 + 3 = 8x are consistent or not.​

Answer 1

Answer:

Step-by-step explanation:

Given :  x² - 4x  + 1.5  = 0 and  2x² - 8x  +  3 = 0

To find :  Equations are consistent or not

Solution:

x² - 4x  + 1.5  = 0

2x² + 3 = 8x

=> 2x² - 8x  +  3 = 0

Dividing by 2 on both sides

=> x² - 4x  + 1.5  = 0

Hence both equations are same so both Equations have same solution

System of equations is called consistent if there is at least one set of values  that satisfies each equation in the system

x = (4  ± √10)/2     for both Equations

=> Hence Equations are consistent

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Answer 2

Answer:

Yes. They are consistent

Step-by-step explanation:

Clearly, 2$x^{2}$+3=8x can be written as 2$x^{2}$-8x+3=0

Also, $x^{2}$-4x+1.5 = 0 can be written as 2$x^{2}$-8x+3=0 by multiplying the whole equation with 2 on both sides

As both these equations are equal, they are consistent