Question

please can you solve both and send the pic​

Answer 1

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

Answer 2

Answer:

don't know the answer please forgive me

Step-by-step explanation:

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