Question

solve all questions step by step​

Answer 1

Step-by-step explanation:

1)Since, given that :-

x - y = 4

and , xy = 45 days

then , we have to find :

x³ - y³ = ?

so , we know that ,

(x - y)³ = x³ - y³ - 3xy (x - y)

using this identity ,

substitute the values given ,

=> (4)³ = x³ - y³ - 3 (45)(4)

Solve the terms,

=> 4 × 4 × 4 = x³ - y³ - 3 × 45 × 4

=> 64 = x³ - y³ - 540

take the like terms to RHS , i.e.,

=> x³ - y³ = 64 + 540

=> x³ - y³ = 604 ...answer

2)3^(x+y)=81

x+y=log3(81)=4

81^(x-y)=3

x-y=log81(3)=1/4=0.25

so the equation system simply is:

x+y=4

x-y=0.25

adiing both gives us

2x=4.25

x=2.125

putting that into the second equation gives us

2.125-y=0.25

y=2.125–0.25=1.875

so the answer is

x=2.125 y=1.875

and yeah, I let google find the log81(3) for me.

evn though it’s obvious since

3^4=81 aka

3=4th root of(81)=81^(1/4)