Flag 8 grade maths> If abc+ab+bc+ca+a+b+c = 1000 then find th...
question mark

If abc+ab+bc+ca+a+b+c = 1000 then find the value of a+b+c?

Divya Ranjan Pattanaik , 8 Years ago
Grade 8
anser 1 Answers
Nishant Vora

Last Activity: 8 Years ago

Dear student,

(a+1)(b+1)(c+1) = a+d+c+ab+bc+ca+abc+1

So we can rewrite this equation
a+b+c+ab+bc+ca+abc=1000

as

(a+1)(b+1)(c+1) - 1 = 1000
so
(a+1)(b+1)(c+1) = 1001

which can be re written as
(a+1)(b+1)(c+1) = 7*11*13

if you look at this eqn closesly, these 7, 11 and 13 are prime numbers and can be rewritten as (6+1)*(10+1)*(12+1)

So you can find that a+b+c = 28.

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments