IIT JEE , AIEEE Forum - Mathematics , Algebra

supriyatomar90

the total no. of terms in (x+y)^200 +(x-y)^200 after simplification (^....raise to power)

the sum of rational terms in the expansion of (sq. root of 2 + 5 th root of 3)raise to power 10 is.........

akhil_o

1)
all equivalent terms are of equal magnitude..
(x-y)^200 has 100 -ve and 101 +ve terms
the negative terms cancel out and equal postve terms add up
so terms=101

sboosy

(2^1/2+ 3^1/5 )¹⁰

a =2^1/2_,b = 3^1/5

t_r+1 = nC_r a^(n-r) b^r

for r = 0 we get 2^1/2power 10 and the other term power 0 which is rational

now for further r values for the term to b rational

it shud be a multiple of 5 since we have 3^1/5

so we take r = 5

but r = 5 means first term is (

2)⁵which is irrational

so now r =10

i think there r the only two terms

hence sum =

(

2)¹⁰+ 3^{1/5 * 10}

= 32 + 9 = 41

But pls correct me if wrong

supriyatomar90

u r right....thanx a lot

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