Question

express x²-8x+5 in the form (x-a)²-b where a and b are integers​

Answer 1

Answer:

Completing the square

x^2 - 8x = -5

x^2 -8x +16 =-5 +16

( x-4)^2 = 11

x^2 - 8x+5 = (x-4)^2 -11

Answer 2

Answer:

The required form is (x - 4)² - 11.

Step-by-step explanation:

Concept:-

• Write the given equation in such a way that the constant value is on the right hand.
• Then make the coefficient of x² equals to 1.
• Now, add the square of half of the coefficient of x on both the sides.

Given:-

x² - 8x + 5 = 0

To express:-

The given equation in (x - a)² - b form where a and b are integers.

Consider the given equation as follows:

x² - 8x + 5 = 0

Shift the constant value to the right-hand side as follows:

x² - 8x = -5

Notice that the coefficient of x² is equal to 1.

So,

Add the square of half of the coefficient of x on both the sides, i.e.,

Add the number 4² on both the sides.

⇒ x² - 8x + 4² = -5 + 4²

⇒ x² - 2(2)x + 4² = -5 + 16

⇒ (x - 4)² = 11 (Since a² + b² - 2ab = (a - b)²)

⇒ (x - 4)² - 11 = 0

Final answer: The equation x² - 8x + 5 in the (x - a)² - b form is (x - 4)² - 11.

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