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CGP EDU Academic Team
Published on: August 14, 2026
Find the real value of x such that x 2 + 2x, 2x + 3 and x 2 + 3x + 8 are lengths of the sides of a triangle
Text Solution
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x > 5
Sol.
For Δ ABC a + b > c, b + c > a, c + a > b
x 2 + 4x + 3 > x 2 + 3x + 8 ⇒ x > 5
x 2 + 5x + 11 > x 2 + 2x ⇒ x > 
2x 2 + 5x + 8 > 2x + 3 ⇒ 2x 2 + 3x + 5 > 0 ⇒ x ∈ R
Common to all is x > 5.
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