Question

solve no.1
through completing the square​

Answer 1

Solution

Given:-

• Equation, 2x² - 7x + 3 = 0,
• 2x² + x - 4 = 0 ,

Find :-

• Roots by Completing square method.

Explantion

Take first Equation

==> 2x² - 7x + 3 = 0

==> 2x² - 7x = -3

divide by 2 in both side,

==> 2x²/2 - 7x/2 = -3/2

==> x² - 7x/2 = -3/2

Add both side, 49/16

==> x² - 7x/2 + 49/16 = -3/2 + 49/16

==> x² - 2 × x × 7/4 + (7/4)² = (-3×8+49)/16

Using Formula

★(a+b)² = a² + b² + 2ab

==> (x - 7/4)² = (-24+49/16

==> (x - 7/4)² = 25/16

==> (x - 7/4) = √(25/16)

==> (x - 7/4) = ± 5/4

First take (- ve) sign.

==> x - 7/4 = -5/4

==> x = -5/4 + 7/4

==> x = (-5 + 7)/4

==> x = 2/4

==> x = 1/2

Again, take (+ve) sign

==> x - 7/4 = 5/4

==> x = 5/4 + 7/4

==> x = (5+7/4

==> x = 12/4

==> x = 3 .

Since

• Roots will be of Equation, 2x² - 7x + 3 = 0, is 1/2 , 3

______________________

Now, Take second Equation,

==> 2x² + x - 4 = 0

==> 2x² + x = 4

Divide by 2 in both side.

==> 2x²/2 + x/2 = 4/2

==> x² + x/2 = 2

Add. 1/16 in both side.

==> x² + 2 × x × 1/4 + 1/16 = 2 + 1/16

==> x² + 2 × x × 1/4 + (1/4)² = (32 + 1)/16

==> (x + 1/4)² = 33/16

==> (x + 1/4) = ±√(33/16)

take (-ve) sign.

==> (x + 1/4) = -√(33/16)

==> x + 1/4 = -√33/4

==> x = (-√33)/4 - 1/4

==> x = (-√33 - 1)/4

==> x = -(√33 + 1)/4

We have,

• √33 = 5.75

==> x = -(5.65 + 1)/4

==> x = - 6.65/4

==> x = 1.67

Again , take (+ve) sign

==> x + 1/4 = √33/4

==> x = √33/4 - 1/4

==> x = (√33 - 1)/4

==> x = (5.65 - 1)/4

==> x = 4.65/4

==> x = 1.17

Since

• roots of Equation, 2x2 + x - 4 = 0, be 1.67, 1.17

__________________

Answer 2

Step-by-step explanation:

Refer to the above attachment

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