What is the value of 2a-b

Answer:

The answer is 13.

Step-by-step explanation:

(b) Find the value of 2a + b: Remember that 2a means 2 × a. Replacing a by 4 and b by 7 gives 2×4 + 7.

Two possible values for 2a - b are 4i√2 and -4i√2, where 'i' is the imaginary unit.

To find the value of 2a - b, we need to eliminate 'b' from the two equations given.

Given equations:

1. 2a + b = 4

2. ab = -3

Let's solve for 'a' and 'b' using these equations.

Step 1: Solve for 'b' in terms of 'a' from equation (1).

2a + b = 4

b = 4 - 2a

Step 2: Substitute the value of 'b' from step 1 into equation (2).

a(4 - 2a) = -3

[tex]4a - 2a^2 = -3[/tex]

Step 3: Rearrange the equation to a quadratic form:

[tex]2a^2 - 4a + 3 = 0[/tex]

Step 4: Solve the quadratic equation for 'a'. You can use the quadratic formula:

a = [ -(-4) ± √([tex](-4)^2[/tex] - 4*2*3) ] / (2*2)

a = [ 4 ± √(16 - 24) ] / 4

a = [ 4 ± √(-8) ] / 4

a = [ 4 ± 2i√2 ] / 4

a = 1 ± i√2

Now we have two possible values for 'a': a = 1 + i√2 and a = 1 - i√2, where 'i' is the imaginary unit (√(-1)).

Step 5: Find the corresponding values of 'b' using the equation b = 4 - 2a.

For a = 1 + i√2:

b = 4 - 2(1 + i√2) = 4 - 2 - 2i√2 = 2 - 2i√2

For a = 1 - i√2:

b = 4 - 2(1 - i√2) = 4 - 2 + 2i√2 = 2 + 2i√2

Now we have two sets of values for 'a' and 'b':

1. a = 1 + i√2, b = 2 - 2i√2

2. a = 1 - i√2, b = 2 + 2i√2

Step 6: Calculate the value of 2a - b for each set of values:

For a = 1 + i√2, b = 2 - 2i√2:

2a - b = 2(1 + i√2) - (2 - 2i√2)

        = 2 + 2i√2 - 2 + 2i√2

        = 4i√2

For a = 1 - i√2, b = 2 + 2i√2:

2a - b = 2(1 - i√2) - (2 + 2i√2)

        = 2 - 2i√2 - 2 - 2i√2

        = -4i√2

So, the two possible values for 2a - b are 4i√2 and -4i√2, where 'i' is the imaginary unit.

To know more about imaginary unit, refer here:

https://brainly.com/question/29274771

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