Question
If ab + bc + ca = 0 Find the value of
1/(a2 - bc) + 1/(b2 - ca) + 1/(c2 - ab)Solution
ab + bc + ca = 0 bc = - ab – ca ca = - ab – bc ab = -bc –ca Now, 1/(a2 - bc) + 1/(b2 - ca) + 1/(c2 - ab) = 1/(a2 - (-ab - ca)) + 1/(b2 - (-ab - bc)) + 1/(c2 - (-bc-ca)) =1/(a2 + ab+ca) + 1/(b2 + ab+bc) + 1/(c2 + bc+ca) = 1/(a(a + b + c)) + 1/(b(a + b + c)) + 1/(c(a + b + c)) = (bc + ca + ab)/(abc(a + b + c)) = 0/(abc(a + b + c)) = 0
Find the value of the given expression-
(4x+4 -5× 4x+2) / 15×4x – 22×4x
If x2 – 10x + 20 = 0, then find the value of (x – 3)2 + 1/(x – 3)2
If x + y = 4 and (1/x) + (1/y) = 24/7, then the value of (x3 + y3).
If x, y and z are real numbers such that (x-5)2+(y-8)2+(z-12)2= 0 then (x+y+z) is equal to
If x + y = 12 and x² + y² = 74, find xy.
If p = 27 - q - r and pq + r(q + p) = 168, then find the value of (p² + q² + r²).
If (x + y) = 6 and (x2 + y2) = 20, then the value of (x – y)2 is equal to:
A takes 8 hours more than the time taken by B to cover a distance of 160 km. If A doubles his speed. he takes 3 hours more than B to cover the same dist...
If x:y:z = 3:4:6, and (5x + 3z) = 132, then find the value of '3y'.
Relevant for Exams:
