f(x)=1/√x e g(x)=x²
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Soluções para a tarefa
Resposta:
\mathbf{a)~y^{2}~-~49}a) y
2
− 49
\mathbf{b)~x^{2}~-~9}b) x
2
− 9
\mathbf{c)~9x^{2}~-~4}c) 9x
2
− 4
\mathbf{d)~25x^{2}~-~16}d) 25x
2
− 16
\mathbf{e)~9x^{2}~-~y}e) 9x
2
− y
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Para resolver o produto da soma pela diferença basta elevar o primeiro e o segundo termo ao quadrado, em seguida colocar o sinal de menos entre esses dois resultados.
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Confira as resoluções abaixo:
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\begin{gathered}\mathbf{a)~(y~-~7)~.~(y~+~7)}\\\\~~~~~1^{o}~termo~=~y~\rightarrow~\mathbf{y^{2}}\\\\~~~~~2^{o}~termo~=~7~\rightarrow~\mathbf{7^{2}~=~49}\\\\Resposta~=~\underline{\boxed{\mathbf{\blue{y^{2}~-~49}}}}\end{gathered}
a) (y − 7) . (y + 7)
1
o
termo = y → y
2
2
o
termo = 7 → 7
2
= 49
Resposta =
y
2
− 49
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\begin{gathered}\mathbf{b)~(x~+~3)~.~(x~-~3)}\\\\~~~~~1^{o}~termo~=~x~\rightarrow~\mathbf{x^{2}}\\\\~~~~~2^{o}~termo~=~3~\rightarrow~\mathbf{3^{2}~=~9}\\\\Resposta~=~\underline{\boxed{\mathbf{\blue{x^{2}~-~9}}}}\end{gathered}
b) (x + 3) . (x − 3)
1
o
termo = x → x
2
2
o
termo = 3 → 3
2
= 9
Resposta =
x
2
− 9
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\begin{gathered}\mathbf{c)~(3x~-~2)~.~(3x~+~2)}\\\\~~~~~1^{o}~termo~=~3x~\rightarrow~\mathbf{(3x)^{2}~=~9x^{2}}\\\\~~~~~2^{o}~termo~=~2~\rightarrow~\mathbf{2^{2}~=~4}\\\\Resposta~=~\underline{\boxed{\mathbf{\blue{9x^{2}~-~4}}}}\end{gathered}
c) (3x − 2) . (3x + 2)
1
o
termo = 3x → (3x)
2
= 9x
2
2
o
termo = 2 → 2
2
= 4
Resposta =
9x
2
− 4
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\begin{gathered}\mathbf{d)~(5x~+~4)~.~(5x~-~4)}\\\\~~~~~1^{o}~termo~=~5x~\rightarrow~\mathbf{(5x)^{2}~=~25x^{2}}\\\\~~~~~2^{o}~termo~=~4~\rightarrow~\mathbf{4^{2}~=~16}\\\\Resposta~=~\underline{\boxed{\mathbf{\blue{25x^{2}~-~16}}}}\end{gathered}
d) (5x + 4) . (5x − 4)
1
o
termo = 5x → (5x)
2
= 25x
2
2
o
termo = 4 → 4
2
= 16
Resposta =
25x
2
− 16
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\begin{gathered}\mathbf{e)~(3x~+~y)~.~(3x~-~y)}\\\\~~~~~1^{o}~termo~=~3x~\rightarrow~\mathbf{(3x)^{2}~=~9x^{2}}\\\\~~~~~2^{o}~termo~=~y~\rightarrow~\mathbf{y^{2}}\\\\Resposta~=~\underline{\boxed{\mathbf{\blue{9x^{2}~-~y}}}}\end{gathered}
e) (3x + y) . (3x − y)
1
o
termo = 3x → (3x)
2
= 9x
2
2
o
termo = y → y
2
Resposta =
9x
2
− y
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Portanto, os resultados são:
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\mathbf{a)~y^{2}~-~49}a) y
2
− 49
\mathbf{b)~x^{2}~-~9}b) x
2
− 9
\mathbf{c)~9x^{2}~-~4}c) 9x
2
− 4
\mathbf{d)~25x^{2}~-~16}d) 25x
2
− 16
\mathbf{e)~9x^{2}~-~y}e) 9x
2
− y