Question

Rezolvați in R următoarele ecuații :
a). (3x+4) la puterea a 2-a =100

b). (3x+1)la puterea a 2-a=121

c). (4x+1)la puterea a 2-a =225

d). (4-7x)la puterea a 2-a=324

Repede dau coroană

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Answer 1

Răspuns: Ai rezolvarea mai jos

Explicație pas cu pas:

Salutare!

$\bf a)~ (3x+4)^{2} =100$

$\bf (3x+4)^{2} =10^{2}$

$\bf 3x+4 =\pm 10 \implies$

$\bf 3x+4 =10 \implies 3x = 10-4\implies 3x = 6~~\bigg|:3 \implies\boxed{\bf x_{1} = 2}$

$\bf 3x+4 =-10 \implies 3x = -10-4\implies 3x = -14 \implies\boxed{\bf x_{2} =-\dfrac{14}{3}}$

$\it~~$

$\bf b)~ (3x+1)^{2} =121$

$\bf (3x+1)^{2} =11^{2}$

$\bf 3x+1 =\pm 11\implies$

$\bf 3x+1 = 11\implies 3x = 11-1\implies 3x = 10\implies \boxed{\bf x_{1}= \dfrac{10}{3}}$

$\bf 3x+1 = -11\implies 3x = -11-1\implies 3x = -12\implies \boxed{\bf x_{2}=-4}$

$\it~~$

$\bf c)~ (4x+1)^{2} =225$

$\bf (4x+1)^{2} =15^{2}$

$\bf 4x+1 =\pm 15\implies$

$\bf 4x+1 = 15\implies 4x = 15-1\implies 4x = 14\implies \boxed{\bf x_{1}= \dfrac{7}{2}}$

$\bf 4x+1 = -15\implies 4x = -15-1\implies 4x = -16\implies \boxed{\bf x_{2}=-4}$

$\it~~$

$\bf d)~ (4-7x)^{2} =324$

$\bf (4-7x)^{2} =18^{2}$

$\bf 4-7x =\pm18 \implies$

$\bf 4-7x = 18\implies -7x = 18-4\implies -7x = 14\implies \boxed{\bf x_{1}= -2}$

$\bf 4-7x = -18\implies -7x = -18-4\implies -7x = -22\implies \boxed{\bf x_{2}= \dfrac{22}{7} }$

PS: Daca esti pe telefon, te rog sa glisezi spre dreapta pentru a vedea rezolvarea completa

Bafta !

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