please can you solve both and send the pic
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Answer:Answers of 1 and 2 are 613 and 702 respectively
Step-by-step explanation:
Q1:- Given a-b=7 and a^2+b^2=85
To find a^3 - b^3
Sol:- firstly by the identity (a-b)^2=a^2 + b^2 -2ab
So,
(a-b)^2=a^2 +b^2 -2ab
(7)^2 (as given a-b=7)= 85(as given a^2 +b^2=85) -2ab
49-85=-2ab
-36=-2ab
36=2ab (as minus on left as well as on right hand side got cancelled
by each other)
then
36/2=ab
ab=18 ...(1)
Now,
by the identity a^3 - b^3 = (a-b)(a^2 +b^2 +ab)
now putting a-b =7(given) ; a^2+b^2=85(given) and ab= 18 (from eq. 1 above)
then
a^3-b^3= 7 x 85+18
a^3-b^3= 595+18
a^3-b^3=613
now your next question
Q2:- Given x+1/x=9
Firstly by the identity (a + b)^2= a^2 + b^2 +2ab
So,
(x+1/x)^2=x^2 + 1/x^2 + 2 * x*1/x
(9)^2(as x+1/x = 9)=x^2+1/x^2 + 2 (as x cancelled the x in division)
81=x^2+1/x^2+2
81 - 2= x^2 +1/x^2
hence,
x^2 + 1/x^2=79 ...... (1)
Now by the identity a^3+b^2 = (a+b)(a^2 + b^2 - ab)
now
x^3+1/x^3= (x+1/x)(x^2+1/x -x*1/x)(given that x+1/x=9 and x^2 + 1/x^2 = 79 from eq. 1)
x^3+1/x^3 = 9 x 79 -1 (x got cancelled by the x in division)
x^3+1/x^3=702
Hope, it helps
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Answer:
don't know the answer please forgive me
Step-by-step explanation:
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