Rozwiąż układ równań x + y=401/x + 1/y=10.... Question from @justyna03031995

justyna03031995 @justyna03031995

October 2018 1 8 Report

Rozwiąż układ równań

x + y=40

1/x + 1/y=10

Józekkk

x+y=40

1 1

-- + ---=10

x y

y=40-x

1 1

--- + ---- =10

x 40-x

40-x+x

-----------= 10

40x- x²

-----------= 10

40x- x²

-----------=1

40x- x²

4=40x-x²

x²-40x+4=0

Δ=b²-4ac

Δ=40²-4·1·4

Δ=1600-16=1584

√Δ=√1584=√11·144=12√11

-b-√Δ

x₁=----------

-b+√Δ

x₂=--------

40 -12√11

x₁=----------=20- 6√11

40+12√11

x₂=----------=20+ 6√11

y=40-x

y₁=40-(20-6√11)

y₁=20+6√11

y₂=40-(20+6√11)

y₂=20-6√11

odp

x₁=20-6√11

x₂=20+6√11

y₁=20+6√11

y₂=20-6√11

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