Home
Class 12
MATHS
If (1+x-2x^2)^6=1+a1x+a2x^(12)++a(12)x^(...

If `(1+x-2x^2)^6=1+a_1x+a_2x^(12)++a_(12)x^(12),` then find the value of `a_2+a_4+a_6++a_(12)dot`

Text Solution

Verified by Experts

The correct Answer is:
31
`(1+x-2x^(2))^(6) = 1+a_(1)x+a_(2)x^(2)+"…."+a_(12)x^(12)`
Putting `x = 1` and `x = - 1` and adding the results, we get
`64 = 2(1+a_(2)+a_(4)+"….")`
`:. a_(2)+a_(4)+a_(6)+"…."a_(12) = 31`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.5|8 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.6|10 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.3|7 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

If (1+x-2x^(2))^(6)=1+a_(1)x+a_(2)x^(12)+...+a_(12)x^(12) then find the value of a_(2)+a_(4)+a_(6)+...+a_(12)

(1+x-2x^(2))^(6)=1+a_(1)x+a_(2)x^(2)+a_(2)x^(3)+....., then the value of a_(2)+a_(4)+a_(6)+......+a_(12) will be (a) 32 (b) 31 (c) 64 (d) 1024

If (1 + x + x^(2) + x^(3))^(n)= a_(0) + a_(1)x + a_(2)x^(2) + a_(3) x^(3) +...+ a_(3n) x^(3n) , then the value of a_(0) + a_(4) +a_(8) + a_(12)+….. is