IIT JEE , AIEEE Forum - Mathematics , Algebra

danny_007

1)in the expansion of (a^1/3 + b^1/9)⁶⁵⁶¹, a and b are prime numbers , find the number of irrational terms

2)suppose the sides of a triangle are three consecutive integers , and one of integer is twice the other , number of such triangles is?

jeesucks

answer is 5832

jeesucks

1- with sides 2,3,4

pinnacle

i suppose sides can also be
1 2 nd 3

jeesucks

it cant because for any triangle a+b>c..................here 1+2=3.........therefore they will make a line

pinnacle

oh ok srry

danny_007

yaa sorry got the answer 1....

rational tems 730 na/

danny_007

so irrational 5832

jeesucks

thats what i reply..........pls read it again..and rate

chimanshu_007

ans 2

make a triangle 1st... with sides ABC

CD = ab / a + c

AD = bc / a + c

triangle ABC and BDC are similar

BC/AC = CD/BC

a² = ((ab)/a+c).b

or b² = a (a+c)........(i)

as it is given b > a

so b can be a + 1 or a + 2

if we take b = a + 1

we get

(a + 1)² = (a + c) a

c = 2 + (1/a)

as c is an integer

a = 1 , b = 2 , c = 3.....

it wont form triangle

if b = a + 2

then c = a + 1 (look @ the given condition)

so

(a + 2)² = a(2a + 1)

solve it....

we get a = 4 , b = 6 c = 5

THATS THE ANSWER :)

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