If a,b : b,c : c,a are the roots of x2−4x+3=0, x2−8x+15=0 and x2−6x+5=0 respectively. Compute [a2+c2a2+b2b2+c2a2+c2]+[2ac−2ab−2bc−2ac]

x2−4x+3=0⇒x=1,3 x2−8x+15=0⇒x=3,5 x2−6x+5=0⇒x=5,1 ∴a=1,b=3,c=5Now [(a+c)2(a−b)2(b−c)2(a−c)2]=[364416]

If a,b : b,c : c,a are the roots of x2−4x+3=0, x2−8x+15=0 and x2−6x+5=0 respectively. Compute [a2+c2a2+b2b2+c2a2+c2]+[2ac−2ab−2bc−2ac]

x2−4x+3=0⇒x=1,3 x2−8x+15=0⇒x=3,5 x2−6x+5=0⇒x=5,1 ∴a=1,b=3,c=5Now [(a+c)2(a−b)2(b−c)2(a−c)2]=[364416]

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If $a, b : b, c : c, a$ are the roots of $x^{2} - 4 x + 3 = 0$ , $x^{2} - 8 x + 15 = 0$ and $x^{2} - 6 x + 5 = 0$ respectively. Compute $[\begin{matrix} a^{2} + c^{2} & a^{2} + b^{2} \\ b^{2} + c^{2} & a^{2} + c^{2} \end{matrix}] + [\begin{matrix} 2 a c & - 2 a b \\ - 2 b c & - 2 a c \end{matrix}]$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$[\begin{matrix} 6 & 4 \\ 4 & 16 \end{matrix}]$

$[\begin{matrix} 36 & 4 \\ 4 & 16 \end{matrix}]$

$[\begin{matrix} - 36 & 4 \\ 4 & - 16 \end{matrix}]$

$[\begin{matrix} 16 & - 4 \\ - 4 & 36 \end{matrix}]$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$x^{2} - 4 x + 3 = 0 \Rightarrow x = 1, 3$
$x^{2} - 8 x + 15 = 0 \Rightarrow x = 3, 5$
$x^{2} - 6 x + 5 = 0 \Rightarrow x = 5, 1$
$∴ a = 1, b = 3, c = 5$
Now $[\begin{matrix} {(a + c)}^{2} & {(a - b)}^{2} \\ {(b - c)}^{2} & {(a - c)}^{2} \end{matrix}] = [\begin{matrix} 36 & 4 \\ 4 & 16 \end{matrix}]$