Question

if distance between points (3, 2) and (-1,x) is 5 then x is equal to​

Answer 1

We are given that the distance between P(3, 2) and Q(-1, x) is equal to 5.

Now, According to question,

√(-1-3) ^2+(x-2) ^2=5

=>(-4) ^2+(x^2+4-4x) =(5)^2

=>16+4+x^2-4x=25

=>x^2-4x-5=0

=>x^2-5x+x-5=0

=>x(x-5) +1(x-5) =0

=>(x+1)(x-5) =0

So, x has two roots

x=(-1) and x=5

Answer 2

Answer:

x = 5

Step-by-step explanation:

√(3-(-1)^2 + (2-x)^2 = 5

= 4^2 + (2-x)^2 = 25

= 16 + 4 - 4x +x^2 = 25

= 20 - 4x + x^2 = 25

= x^2 - 4x - 5 = 0

Splitting the middle term

= x^2 - 5x + x - 5

To obtain roots of this equation, factorization

= x(x-5) + 1(x-5)

= (x+1)(x-5)

Therefore x = -1 (&)(or) x = 5