If (a+b)=8,a2+b2=40find the value of a3+b3
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Answered by
65
(a+b)2=a2 +b2 +2ab
(8)2= 40+2ab
64=40+2ab
64-40=2ab
24= 2ab
24÷2=ab
12=ab
(a+b)3= a3+ b3+3ab (a+b)
(8)3= a3+b3+3*12(a+b)
(8)3= a3+b3+ 36(a+b)
(8)3=a3+b3+36*8
(8)3=a3+b3+288
(8)3-288=a3+b3
512-288=a3+b3
224=a3+b3
(8)2= 40+2ab
64=40+2ab
64-40=2ab
24= 2ab
24÷2=ab
12=ab
(a+b)3= a3+ b3+3ab (a+b)
(8)3= a3+b3+3*12(a+b)
(8)3= a3+b3+ 36(a+b)
(8)3=a3+b3+36*8
(8)3=a3+b3+288
(8)3-288=a3+b3
512-288=a3+b3
224=a3+b3
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(a+b+c)=12a2+b2+c2=90find the value of a3+b3+c3-3abc
please anser fast
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i think that the question is wrong because it says -3abc??
ok wait..i know
squaring both the sides we get (a+b+c)2=12*12 a2+b2+c2+2ab+2bc+2ca=144. 90 +2(ab+bc+ca)=144. 2(ab+bc+ca)=144-90=54.ab+bc+ca=54÷2. Now use this identity a3+b3+c3-3abc= (a+b+c)(a2+b2+c2-ab-bc+ca). 12[90-(ab+bc+ca)] . 12[90-27] .12*63=756
Answered by
17
(a+b)3=a3+b3+3ab(a+b) so, to find a3 and b3 we have only. (a+b)=8 , a2+b2=40.. So we need to find the value of (ab) to get the value of a3+b3 .. so, (a+b)2=a2+2ab+b2. (a+b)2=a2+b2+2ab. (8)2=40+2ab. 64=40+2ab. 64-40=2ab. 24=2ab. 24/2=ab. 12=ab. now we got the value of (ab) so, (a+b)3=a3+b3+3ab(a+b). (8)3=a3+b3+3*12(8). 512=a3+b3+36(8). 512=a3+b3+ 288. 512-288=a3+b3. 224=a3+b3. therefore a3+b3=224
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