if a+b=10 and ab=21 find the value of a³ +b³
if a + b is equal to 10 and ab is equal to 21 find the value of a cube plus b cube
Solution:-
Let x=a³ +b³ .............. (1)
and given a+b=10 and ab=21
Now from (1)
x=a³ +b³
=(a+b) (a^2 - ab +b^2)
=(a+b) (a^2+b^2 -ab)
=(a+b) {(a+b)^2 -2ab -ab)}
=(a+b) {(a+b)^2 -3ab)}
put value of a+b=10 ab=21
=(10) {(10)^2 -3×21)}
=(10) {(100 - 63)}
=10×37
=370 ans
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if a - b = 4 and ab=21 find the value of a3- b3
Solution:-
Let x=a³ - b³ .............. (1)
and given a+b=10 and ab=21
Now from (1)
x=a³ - b³
=(a-b) (a^2 + ab +b^2)
=(a+b) (a^2+b^2+ ab)
=(a-b) {(a-b)^2 +2ab +ab)}
=(a-b) {(a-b)^2 +3ab)}
put value of a-b=10 ab=21
=(4) {(4)^2+3×21)}
=(4) {(16+ 63)}
=4×79
=316 ans
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if a+b=10 and a2+b2=58 find the value of a3+b3
Solution:-
Let x=a³ +b³ .............. (1)
and given a2+b2=58 and a+b=10
first we find value of ab
we know that
a2+b2 = (a+b)^2 -2ab
58=(10)^2 -2ab
58=100-2ab
58-100=-2ab
-42= -2ab
2ab=42
ab=42/2
ab-=21
Now from (1)
x=a³ +b³
=(a+b) (a^2 - ab +b^2)
=(a+b) (a^2+b^2 -ab)
=(a+b) {(a+b)^2 -2ab -ab)}
=(a+b) {(a+b)^2 -3ab)}
put value of a+b=10 ab=21
=(10) {(10)^2 -3×21)}
=(10) {(100 - 63)}
=10×37
=370 ansif a + b = 10 and ab = 24, then find the value of a3+b3
Solution:-
Let x=a³ +b³ .............. (1)
and given a+b=10 and ab=24
Now from (1)
x=a³ +b³
=(a+b) (a^2 - ab +b^2)
=(a+b) (a^2+b^2 -ab)
=(a+b) {(a+b)^2 -2ab -ab)}
=(a+b) {(a+b)^2 -3ab)}
put value of a+b=10 ab=24
=(10) {(10)^2 -3×24)}
=(10) {(100 - 72)}
=10×28
=280 ans