Question

find the value of x if x+4,2x+8,2x-1 and 3x+2 are in proportion​

Answer 1

x 2 +2x,2x+3, & x 2 +3x+8

are the sides of a triangle

then sum of any two side will always be greater than the third side

(x 2 +2x)+(2x+3)>x 2 +3x+8

⇒x>5 ………(1)

(x 2 +2x)+(x 2 +3x+8)>2x+3

2x 2 +3x+5>0

⇒x∈R (∴a>0,D<0)

(2x+3)+(x 2 +3x+8)>x 2 +2x

3x+11>0

x> 3/−11

So these will be sides of a triangle for x>5.