Question

(15) Rezolvaţi în R următoarele ecuații: a) √10x-13√√2 = 2√2; c) 14√√7-√21x=2√7; e) 2√15-3√10x=8√/15; b) √15x+14√5=5√√5; d) 5√6x+3√10=18/10; f) 9√14-2√√21x=3√14.​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

$\sqrt{10} x-13\sqrt{2} = 2\sqrt{2}$

$\sqrt{10} x=2\sqrt{2}+13\sqrt{2} \iff \sqrt{10} x=15\sqrt{2} \ \ \Big|:\sqrt{10}$

$x = \dfrac{15\sqrt{2}}{\sqrt{10} } = \dfrac{15\sqrt{2} \cdot \sqrt{10} }{10} = \dfrac{30 \sqrt{5} }{10}$

$\implies x = 3\sqrt{5}$

b)

$\sqrt{15} x+14\sqrt{5} =5\sqrt{5}$

$\sqrt{15} x =5\sqrt{5}-14\sqrt{5} \iff \sqrt{15} x =-9\sqrt{5} \ \ \Big|:\sqrt{15}$

$x = -\dfrac{9\sqrt{5}}{\sqrt{15}} = -\dfrac{9\sqrt{5} \cdot \sqrt{15} }{15} = -\dfrac{45\sqrt{3}}{15}$

$\implies x = - 3\sqrt{3}$

c)

$14\sqrt{7}-\sqrt{21}x=2\sqrt{7}$

$-\sqrt{21}x=2\sqrt{7}-14\sqrt{7} \iff -\sqrt{21}x=-12\sqrt{7} \ \ \Big|:(-\sqrt{21})$

$x = - \dfrac{12\sqrt{7}}{\sqrt{21}} = - \dfrac{12\sqrt{7} \cdot \sqrt{21} }{21} = - \dfrac{84\sqrt{3}}{21}$

$\implies x = - 4\sqrt{3}$

d)

$5\sqrt{6}x + 3\sqrt{10} = 18\sqrt{10}$

$5\sqrt{6}x = 18\sqrt{10} - 3\sqrt{10} \iff 5\sqrt{6}x = 15\sqrt{10} \ \ \Big|:5\sqrt{6}$

$x = \dfrac{15\sqrt{10}}{5\sqrt{6}} = \dfrac{15\sqrt{2 \cdot 5} \cdot \sqrt{6} }{5 \cdot 6} = \dfrac{2\sqrt{15}}{2}$

$\implies x = \sqrt{15}$