Question

Quais são os valores do X?​

Answer 1

Explicação passo-a-passo:

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b)

$\sf{ {x}^{2} = {2}^{2} + {3}^{2} } \\ \sf{ {x}^{2} = 4 + 9} \\ \sf{ {x}^{2} = 13 } \\ \red{ \boxed{ \green{ \boxed{ \pink{ \boxed{ \sf{x = \sqrt{13} }} }} } } }$

c)

$\sf{ {x}^{2} = {2 \sqrt{2} }^{2} + { \sqrt{10} }^{2} } \\ \sf{ {x}^{2} = 2 \times 2 + { \sqrt{10} }^{2} } \\ \sf{ {x}^{2} = 2 \times 2 + 10 } \\ \sf{ {x}^{2} = 4 + 10} \\ \sf{ {x}^{2} = 14 } \\ \red{ \boxed{ \green{ \boxed{ \pink{ \boxed{ \sf{x = \sqrt{14} }} }} } } }$

e)

$\sf{ {(x + 9)}^{2} = {(2x)}^{2} + {(x + 3)}^{2} } \\ \sf{ {x}^{2} + 18x + 81 = {(2x)}^{2} + {(x + 3)}^{2} } \\ \sf{ \cancel{\blue { {x}^{2} }}+ 18x + 81 = {(2x)}^{2} + \cancel{\blue { {x}^{2} }} + 6x + 9} \\ \sf{18x + 81 = {(2x)}^{2} + 6x + 9 } \\ \sf{18x + 81 = {4x}^{2} + 6x + 9} \\ \sf{18x + 81 - {4x}^{2} - 6x - 9 = 0 } \\ \sf{12x + 81 - {4x}^{2} - 9 = 0} \\ \sf{12x + 72 - {4x}^{2} = 0} \: \: \: \: \: \div (4) \\ \sf{3x + 18 - {x}^{2} = 0} \: \: \: \: \: \times ( - 1) \\ \sf{ - 3x - 18 + {x}^{2} = 0} \\ \sf{ {x}^{2} - 3x - 18 = 0} \\ \sf{ {x}^{2} + 3x - 6x - 18 = 0} \\ \sf{x(x + 3) - 6(x + 3) = 0} \\ \sf{(x + 3) \times (x - 6) = 0} \\ \sf{x + 3 = 0} \\ \sf{x - 6 = 0} \\ \sf{x = - 3} \\ \sf{x = 6} \\ \red{ \boxed{ \green{ \boxed{ \pink{ \boxed{ \sf{x = 6}} }} } } }$

f)

$\sf{ { \sqrt{26} }^{2} = { \sqrt{17} }^{2} + {x}^{2} } \\ \sf{26 = { \sqrt{17} }^{2} + {x}^{2} } \\ \sf{26 = 17 + {x}^{2} } \\ \sf{ - {x}^{2} = 17 - 26 } \\ \sf{ - {x}^{2} = - 9} \\ \sf{ {x}^{2} = 9} \\ \sf{x = \sqrt{9} } \\ \red{ \boxed{ \green{ \boxed{ \pink{ \boxed{ \sf{x = 3}} }} } } }$