Question

Find the value of x. The distance between (4,x) and (-5,8) is √155​

Answer 1

Answer:

x=16.602

or

x= -0.602

Step-by-step explanation:

$\sqrt{(-5-4)^2+(8-x)^2} = \sqrt{155}$

$\sqrt{(-9)^2+8^2+x^2-16x} =\sqrt{155}$

$\sqrt{81+64+x^2-16x} =\sqrt{155}$

$\\81+64+x^2-16x=155$

$145+x^2-16x=155$

$x^2-16x=10$

$x^2-16x-10=0$

$x=\frac{-b\±\sqrt{b^2-4ac} }{2a}$

$x=\frac{16\±\sqrt{256+40} }{2}$

$x=\frac{16\±\17.204}{2}$

$x=\frac{16+17.204}{2}$  $or$  $x=\frac{16-17.204}{2}$

$x=16.602$  $or$  $x=-0.602$

Answer 2

Answer:

Distance = √ 155

Distance = √ (x 2 - x 1)^2 + (y 2 - y 1)^2

Distance = √ (8 - x)^2 + (- 5 - 4)^2

Distance = √ 64 - 16 x + x^2 + 81

√155 = √ 64 - 16 x + x^2 + 81

On squaring both sides we get,

155 =  64 - 16 x + x^2 + 81

x^2 - 16 x - 10 = 0

Using Shri Dharacharya,

x =(16+√296)/2=8+√ 74 = 16.602 or

x =(16-√296)/2=8-√ 74 = -0.602

So, x = 17 or -1

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