The equation |(1+x)2 (1-x)2 -(2+x2) 2 x+1 3 x 1-5 x x+1 2 x 2-3 x|+|(1+x)2 2 x+1 x+1 (1-x)2 3 x 2 x 1-2 x 3 x-2 2 x-3|=0

Question

The equation |(1+x)2 (1-x)2 -(2+x2) 2 x+1 3 x 1-5 x x+1 2 x 2-3 x|+|(1+x)2 2 x+1 x+1 (1-x)2 3 x 2 x 1-2 x 3 x-2 2 x-3|=0 (A) has no real solution (B) has 4 real solutions (C) has two real and two non-real solutions (D) has infinite number of solutions, real or non-real

Tardigrade Admin · Accepted Answer

1 text st two columns of 1 text st determinant are same as 1 text st two rows of 2 text nd . Hence transpose the 2 text nd . Add the two determinants and use C 1 arrow C 1+ C 3 ⇒ D =0

Q. The equation $∣ ∣ (1 + x)^{2} 2 x + 1 x + 1 (1 - x)^{2} 3 x 2 x - (2 + x^{2}) 1 - 5 x 2 - 3 x ∣ ∣ + ∣ ∣ (1 + x)^{2} (1 - x)^{2} 1 - 2 x 2 x + 1 3 x 3 x - 2 x + 1 2 x 2 x - 3 ∣ ∣ = 0$

has no real solution

has 4 real solutions

has two real and two non-real solutions

has infinite number of solutions, real or non-real

$1^{st}$ two columns of $1^{st}$ determinant are same as $1^{st}$ two rows of $2^{nd}$ .
Hence transpose the $2^{nd}$ . Add the two determinants and use $C_{1} \to C_{1} + C_{3} \Rightarrow D = 0$

Q. The equation ∣∣​(1+x)22x+1x+1​(1−x)23x2x​−(2+x2)1−5x2−3x​∣∣​+∣∣​(1+x)2(1−x)21−2x​2x+13x3x−2​x+12x2x−3​∣∣​=0