Home
Class 12
MATHS
Find (x+a)^(3)-(x-a)^(3). Hence evaluate...

Find `(x+a)^(3)-(x-a)^(3)`. Hence evaluate `(sqrt(5)+sqrt(4))^(3)-(sqrt(5)-sqrt(4))^(3)`

Text Solution

Verified by Experts

`(x+a)^(3)-(x-a)^(3)`
`={.^(3)C_(0)x^(3)+.^(3)C_(1)x^(2)a+.^(3)C_(2)xa^(2)+.^(3)C_(3)a^(3)}-{.^(3)C_(0)x^(3)-.^(3)C_(1)x^(2)a+.^(3)C_(2)xa^(2)-.^(3)C_(2)a^(3)}`
Hence, `(x+a)^(3)-(x-a)^(3)=2{.^(3)C_(1)x^(2)a+.^(3)C_(3)a^(3)}` . . . (1)
Now put the value of x and a as `sqrt(5) and sqrt(4)` respectively, we get
`(sqrt(5)+sqrt(4))^(3)-(sqrt(5)-sqrt(4))^(3)=2{.^(3)C_(1)(sqrt(5))^(2)sqrt(4)+.^(3)C_(2)(sqrt(4))^(3)}`
`=2{3xx5sqrt(4)+4sqrt(4)}=2{15sqrt(4)+4sqrt(4)}`
`=38sqrt(4)=76`
`therefore(sqrt(5)+sqrt(4))^(3)-(sqrt(5)-sqrt(4))^(3)=76`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    AAKASH INSTITUTE|Exercise Illustration|1 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE|Exercise Try Yourself|20 Videos

  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise section-J (Aakash Challengers Qestions)|16 Videos

Similar Questions

Explore conceptually related problems

Find (x+a)^(5)+(x-a)^(5) . Hence, evaluate (sqrt(6)+sqrt(7))^(5)+(sqrt(6)-sqrt(7))^(5)

Find (a+b)^(4)-(a-b)^(4). Hence evaluate (sqrt(3)+sqrt(2))^(4)-(sqrt(3)-sqrt(2))^(4)

Evaluate (sqrt(5)-sqrt(3))/(sqrt(5)-sqrt(3))

(sqrt(x)+sqrt(3))^(4)+(sqrt(x)-sqrt(3))^(4)

Find quad (a+b)^(4)-(a-b)^(4) Hence,evaluate (sqrt(3)+sqrt(2))^(4)-(sqrt(3)-sqrt(2))^(4)

Evaluate (4+sqrt(5))(sqrt(3)-sqrt(7))

Evaluate (sqrt(3)+sqrt(3))(3+sqrt(5))

Evaluate : ( sqrt(5) + sqrt(3) )/ ( sqrt(5) - sqrt(3))

Evaluate |[sqrt(3), sqrt(5)],[-sqrt(5), 3sqrt(3)]|

Find x (x^(sqrt(5)+sqrt(3)))^(sqrt(5)-sqrt(3))=9