Question

If x^2-(a+b)x+ab=0,
then what is the value of (x-a)^2+(x-b)^2​

Answer 1

Answer:

0

Step-by-step explanation:

→ x² - (a + b)x + ab = 0

→ x² - ax - bx + ab = 0

→ x(x - a) - b(x - a) = 0

→ (x - a)(x - b) = 0

Each getting “0”, therefore

→ (x - a) = 0 and (x - b) = 0

→ (x - a)² = 0 and (x - b)² = 0

→ (x - a)² + (x - b)² = 0

Hence final result will be 0 only.

Answer 2

Let's first of all write the question clearly;

If x² - (a + b) x + ab = 0,  then what is the value of (x - a)² + (x - b)²​?

Here;

So, to start solving this question let's Simplify the equation x² - (a + b)x + ab = 0;

x² - (a + b)x + ab = 0

Firstly let's get rid of the parenthesis;

x² - ax + bx + ab = 0

Now let's take (x - a) as common;

x (x - a) - b (x - a)

Simplify;

(x - a) (x - b) = 0

Since, equation is equal to zero, then (x - a) and (x + b) = 0

How?? So, to find how let's divide (x - b) from both the sides;

$\dfrac{\text{(x - a) }\cancel{\text{(x - b)}}}{\cancel{\text{(x - b)}}} = \dfrac{0}{\text{(x - b)}}$

Simplify;

We get, (x - a) = 0 and If we divide (x - a) from both sides, we get (x - b) = 0.

So, let's continue;

Yup, So Let's plugging the value of (x - a) and (x - b) in the equation (x - a)² - (x - b)² = ?

(x - a)² - (x - b)² = ?

(0)² - (0)²

Simplify;

0 - 0

Solve;

0

Therefore, the value of (x - a)² - (x - b)² = 0