Patience's front

Algebra Level pending

If c c and d d are the roots of the equation x 2 − 10 a x − 11 b = 0 {x^2}-{10ax}-{11b}=0 and a a and b b are the roots of the equation x 2 − 10 c x − 11 d = 0 {x^2}-{10cx}-{11d}=0 then find the value of a + b + c + d {a}+{b}+{c}+{d} .


The answer is 1210.

Anweshan Bor by anweshan bor , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Anweshan Bor
Mar 4, 2016

Clearly, we have c + d = 10 a . 1 {c}+{d}={10a}. _1 And a + b = 10 c . 2 {a}+{b}={10c}. _2 so a + b + c + d = 10 ( a + c ) {a}+{b}+{c}+{d}=10({a}+{c}) now, c x 2 − 10 a c − 11 b = 0 {c}{x^2}-{10ac}-11{b}=0 and a x 2 − 10 a c − 11 d = 0 {a}{x^2}-{10ac}-11{d}=0 On subtracting we get, c 2 − a 2 = 11 ( b − d ) . 3 {c^2}-{a^2}=11({b-d}). _3 From 1-2, we have b − d = 11 ( c − a ) . 4 {b}-{d}=11({c}-{a}). _4 Using 4 in 3 we get a + c = 121 {a}+{c}=121 Hence a + b + c + d = 1210 {a}+{b}+{c}+{d}=1210

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...