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3 years ago

If A(2, x) , B(x, 8) and AB = 3√2 cm, then x = ?

Mathematics

1 answer:

Nuetrik [128]3 years ago

5 0

Answer:

x =5

Step-by-step explanation:

Using the formula for calculating the distance between two points

D = √(x2-x1)²+(y2-y1)²

Given the points A(2, x) , B(x, 8) and AB = 3√2

On substituting the given values into the formula;

AB = √(x-2)²+(8-x)²

3√2= √(x-2)²+(8-x)²

square both sides

(3√2)²= (x-2)²+(8-x)²

18 = (x-2)²+(8-x)²

expand

18 = x²-4x+4+64-16x+x²

18 = 2x²-20x+68

2x²-20x+68-18 = 0

2x²-20x+50 = 0

x²-10x+25 = 0

Factorize

x²-5x-5x+16 = 0

x(x-5)-5(x-5) = 0

(x-5)(x-5) = 0

x-5 = 0 an x-5 = 0

x = 5

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