Let \( \alpha \) and \( \beta \) two real roots of the equation \( (k+1) \tan ^{2} x \) \( -\sqr...

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Let \( \alpha \) and \( \beta \) two real roots of the equation \( (k+1) \tan ^{2} x \) \( -\sqrt{2} \cdot \lambda \tan x=(1-k) \), where \( k(\neq-1) \) and \( \lambda \) are real numbers. If \( \tan ^{2}(\alpha+\beta)=50 \), then a value of \( \lambda \) is
(a) 5
(b) 10
(c) \( 10 \sqrt{2} \)
(d) \( 5 \sqrt{2} \)
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