C6402 tal :29 b c (946)?
Question

# C6402 tal :29 b c (946)?

JEE/Engineering Exams
Maths
Solution
110
4.0 (1 ratings)
( left(begin{array}{ccc}(b+c)^{2} & a^{2} & a^{2} b^{2} & (c+a)^{2} & b^{2} c^{2} & c^{2} & (a+b)^{2}end{array} midright. ) ( c_{1} rightarrow a_{1}-c_{2} ) ( =left|begin{array}{cc}(b+c)^{2}-a^{2} & 0 b^{2}-(a+c)^{2} & (a+c)^{2}-b^{2} 0 & c^{2}-(a+b)^{2} & b^{2} (a+b)^{2}end{array}right| ) ( =left|begin{array}{ccc}(b+c-a)(a+b+c) & 0 & a^{2} (b-a-c)(a+b+c) & (a+c-b)(a+b+c) & b^{2} 0 & (c-a-b)(a+b+c) & (a+b)^{2}end{array}right| ) ( =(a+b+c)^{2}left(begin{array}{ccc}b+c-a & 0 & 0 (b-a-c) & (a+c-b) & 0^{2} 0 & (c-a-b) & (a+c)end{array}right. ) ( R_{2} rightarrow R_{2}-R_{1}, quad R_{3} rightarrow R_{2}-R_{1} ) ( =(a+b+c)^{2}left|begin{array}{ccc}b+c-a & 0 & a^{2} -2 c & a+c-b & b^{2}-a^{2} 2 a-2 b & -2 a & 2 a bend{array}right| ) ( =2(a+b+c)^{2}left|begin{array}{ccc}b+c-a & 0 & a^{2} -2 c & a+c-b & b^{2}-a^{2} a-b & -a & a bend{array}right| ) ( =2(a+b+c)^{2}left{(b+c-a)left|begin{array}{cc}a+c-b & b^{2}-a^{2} -a & a bend{array}right|+a^{2}left|begin{array}{cc}-2 c & x+c-b a-b & -aend{array}right|right}(R, text { expressienn }) ) ( 2(a+b+c)^{2}left{(b+c-a)left(a^{2} b+a b c-a b^{2}+a b^{2}-a^{3}right)+a^{2}left(2 a c-a^{2}-b^{2}+2 a b-a c+b cright)right} ) ( 22(a+b+c)^{6}left{(b+c-a)left(a^{2} b+a b c-a^{5}right)+a^{2}left(a c-b^{2}-b^{2}+2 a b+b cright)right] ) ( =2(a+b+c)^{2}left[a b^{2} c+a^{2} b c+a b c^{2}right] ) ( =2 operatorname{arcc}(a+b+c)^{2}(a+b+c ) ( =2.06 c(a+b+c)^{2} ) key rey maes