If a,b and c are real numbers such that a squared+ 2b = 7 and  b squared+ 4c = -7 and c squared+ 6a = -14 then find a squared+  b squared + c squared

Asked by joshiraghavendra53 | 26th Apr, 2015, 03:48: PM

Expert Answer:

G i v e n space t h a t comma space a squared plus 2 b equals 7 comma space b squared plus 4 c equals negative 7 space a n d space c squared plus 6 a equals negative 14 W e space n e e d space t o space f i n d space t h e space v a l u e space o f space a squared plus b squared plus c squared colon L e t space u s space a d d space t h e space g i v e n space e q u a t i o n s. T h u s comma w e space h a v e comma space a squared plus 2 b plus space b squared plus 4 c plus c squared plus 6 a equals 7 minus 7 minus 14 rightwards double arrow space a squared plus space b squared plus c squared plus 2 b plus 4 c plus 6 a equals negative 14 rightwards double arrow space a squared plus space b squared plus c squared equals negative 14 minus 2 b minus 4 c minus 6 a rightwards double arrow space a squared plus space b squared plus c squared equals negative open parentheses 14 plus 2 b plus 4 c plus 6 a close parentheses S i n c e space a comma space b space a n d space c space a r e space r e a l space n u m b e r s comma space a squared plus b squared plus c squared greater than 0. T h u s comma space minus open parentheses 14 plus 2 b plus 4 c plus 6 a close parentheses greater than 0 T h a t space i s space space a squared plus b squared plus c squared equals negative open parentheses 14 plus 2 b plus 4 c plus 6 a close parentheses rightwards double arrow space a squared plus b squared plus c squared plus 2 b plus 4 c plus 6 a equals negative 14 rightwards double arrow space a squared plus 6 a plus b squared plus 2 b plus c squared plus 4 c equals negative 14 rightwards double arrow space a squared plus 6 a plus b squared plus 2 b plus c squared plus 4 c plus 14 equals 0 rightwards double arrow space a squared plus 6 a plus b squared plus 2 b plus c squared plus 4 c plus 9 plus 1 plus 4 equals 0 rightwards double arrow space a squared plus 6 a plus 9 plus b squared plus 2 b plus 1 plus c squared plus 4 c plus 4 equals 0 rightwards double arrow space open parentheses a plus 3 close parentheses squared plus open parentheses b plus 1 close parentheses squared plus open parentheses c plus 2 close parentheses squared equals 0 rightwards double arrow space open parentheses a plus 3 close parentheses squared equals 0 space a n d space open parentheses b plus 1 close parentheses squared equals 0 space a n d space open parentheses c plus 2 close parentheses squared equals 0 rightwards double arrow space a equals negative 3 space a n d space b equals negative 1 space a n d space c equals negative 2 T h u s comma a squared plus b squared plus c squared equals open parentheses negative 3 close parentheses squared plus open parentheses negative 1 close parentheses squared plus open parentheses negative 2 close parentheses squared equals 14

Answered by Vimala Ramamurthy | 14th May, 2015, 03:27: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.