The expression [x+(x3−1)12]5+[x−(x3−1)12]5 is a polynomial of degree

[x+(x3−1)12]5+[x−(x3−1)12]5 (x+a)n+(x−a)n=2[ nC0xn+ nC2xn−2a2+ nC4xn−4a4+⋯] =[ 5C0x5+ 5C1x4(x3−1)]12+ 5C2[(x3−1)12]2.x3 + 5C3x2[(x3−1)12]3 + 5C4x[(x3−1)12]4+ 5C5[(x3−1)12]5 =[ 5C0x5− 5C1x4(x3−1)12+ 5C2x3((x3−1)12)2− 5C3x2(x3−1)+ 5C4x((x3−1)12)4− 5C5((x3−1)12)5] =2[ 5C0x5+ 5C2x3(x3−1)+ 5C4x(x3−1)2+⋯] Degree is 7.

The expression [x+(x3−1)12]5+[x−(x3−1)12]5 is a polynomial of degree

[x+(x3−1)12]5+[x−(x3−1)12]5 (x+a)n+(x−a)n=2[ nC0xn+ nC2xn−2a2+ nC4xn−4a4+⋯] =[ 5C0x5+ 5C1x4(x3−1)]12+ 5C2[(x3−1)12]2.x3 + 5C3x2[(x3−1)12]3 + 5C4x[(x3−1)12]4+ 5C5[(x3−1)12]5 =[ 5C0x5− 5C1x4(x3−1)12+ 5C2x3((x3−1)12)2− 5C3x2(x3−1)+ 5C4x((x3−1)12)4− 5C5((x3−1)12)5] =2[ 5C0x5+ 5C2x3(x3−1)+ 5C4x(x3−1)2+⋯] Degree is 7.

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

The expression ${[x + {(x^{3} - 1)}^{\frac{1}{2}}]}^{5} + {[x - {(x^{3} - 1)}^{\frac{1}{2}}]}^{5}$ is a polynomial of degree

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

{[x + {(x^{3} - 1)}^{\frac{1}{2}}]}^{5} + {[x - {(x^{3} - 1)}^{\frac{1}{2}}]}^{5}

${(x + a)}^{n} + {(x - a)}^{n} = 2 [^{n} C_{0} x^{n} +^{n} C_{2} x^{n - 2} a^{2} +^{n} C_{4} x^{n - 4} a^{4} + \dots]$

$= {[^{5} C_{0} x^{5} +^{5} C_{1} x^{4} (x^{3} - 1)]}^{\frac{1}{2}} +^{5} C_{2} {[{(x^{3} - 1)}^{\frac{1}{2}}]}^{2} . x^{3}$ $+^{5} C_{3} x^{2} {[{(x^{3} - 1)}^{\frac{1}{2}}]}^{3}$

$+^{5} C_{4} x {[{(x^{3} - 1)}^{\frac{1}{2}}]}^{4} +^{5} C_{5} {[{(x^{3} - 1)}^{\frac{1}{2}}]}^{5}$

$= [^{5} C_{0} x^{5} -^{5} C_{1} x^{4} {(x^{3} - 1)}^{\frac{1}{2}} +^{5} C_{2} x^{3} {({(x^{3} - 1)}^{\frac{1}{2}})}^{2} -^{5} C_{3} x^{2} (x^{3} - 1) +^{5} C_{4} x {({(x^{3} - 1)}^{\frac{1}{2}})}^{4} -^{5} C_{5} {({(x^{3} - 1)}^{\frac{1}{2}})}^{5}]$