Prove that equation has exactly 2 solutions

calculus

Yes, try to divide into cases.

More complete answer :

For $x \in ]- \infty, \lambda_1[$, all your terms are negative -> No solutions

For $x \in ]\lambda_1, \lambda_2[$ -> use the continuity of the function as you said on the try 2

For $x \in ]\lambda_2, \lambda_3[$ -> use the continuity of the function as you said on the try 2

For $x \in ]- \infty, \lambda_3[$, all your terms are positive -> No solutions

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