Advertisements
Advertisements
Question
If a − 2b + 3c = 0; state the value of a3 − 8b3 + 27c3.
Advertisements
Solution
a − 2b + 3c = 0
a3 − 8b3 + 27c3
x3 + y3 + z3 − 3xyz = (x + y + z) (x2 + y2 + z2 − xy − yz − zx)
a3 − (2b)3 + (3c)3 = a3 − 8b3 + 27c3
a3 + (−2b)3 + (3c)3
x + y + z = 0 ⇒ x3 + y3 + z3 = 3xyz
-
x = a
-
y = −2b
-
z = 3c
a − 2b + 3c = 0 ⇒ x + y + z = 0
x3 + y3 + z3 = 3xyz ⇒ a3 + (−2b)3 + (3c)3 = 3(a) (−2b) (3c)
= 3⋅a⋅(−2b)⋅3c = −18abc
a3 − 8b3 + 27c3 = −18abc
APPEARS IN
RELATED QUESTIONS
Simplify : ( x - 6 )( x - 4 )( x + 2 )
Simplify: (x + 6) (x − 4) (x − 2)
Find : (a + b)(a + b)
Prove that : x2+ y2 + z2 - xy - yz - zx is always positive.
If x = 3 + 2√2, find :
(i) `1/x`
(ii) `x - 1/x`
(iii) `( x - 1/x )^3`
(iv) `x^3 - 1/x^3`
If x + 5y = 10; find the value of x3 + 125y3 + 150xy − 1000.
Using suitable identity, evaluate (104)3
Using suitable identity, evaluate (97)3
Evaluate :
`[0.8 xx 0.8 xx 0.8 + 0.5 xx 0.5 xx 0.5]/[0.8 xx 0.8 - 0.8 xx 0.5 + 0.5 xx .5]`
Evaluate :
`[1.2 xx 1.2 + 1.2 xx 0.3 + 0.3 xx 0.3 ]/[ 1.2 xx 1.2 xx 1.2 - 0.3 xx 0.3 xx 0.3]`
