Question

Dau coroana va rog...​

Answer 1

Salutare !!!

Pentru a fi mai usoare calcule vom descompune numerele de sub radical

32 = 2⁵

1024 = 2¹⁰ = 32²

135 = 3³ × 5

1225 = 5² × 7² = 35²

2025 = 3⁴ × 5² = 45²

$\bf\dfrac{\sqrt{32+\sqrt{1024}}}{\sqrt{135-\sqrt{1225}}}=\dfrac{2x}{\sqrt{270-\sqrt{2025}}}$

$\bf\dfrac{\sqrt{32+32}}{\sqrt{135-35}}=\dfrac{2x}{\sqrt{270-45}}$

$\bf\dfrac{\sqrt{64}}{\sqrt{100}}=\dfrac{2x}{\sqrt{225}}$

$\bf\dfrac{\sqrt{8^{2} }}{\sqrt{10^{2} }}=\dfrac{2x}{\sqrt{15^{2} }}$

$\bf\dfrac{{8}}{10}}=\dfrac{2x}{15}}$

$\bf\dfrac{{\not8}}{\not10}}=\dfrac{2x}{15}}$

$\bf\dfrac{{4}}{5}}=\dfrac{2x}{15}}$

$\bf5\cdot2x=4\cdot15$

$\bf 10x=60$

$\bf x=60:10$

$\boxed{\bf x=6}$

Answer 2

$\frac{\sqrt{32+\sqrt{1024}}}{\sqrt{135-\sqrt{1225}}} =\frac{2x}{\sqrt{270-\sqrt{2025}}}$

$\sqrt{1024}=32\\\sqrt{1225}=35\\\sqrt{2025}=45$

$\frac{\sqrt{32+32}}{\sqrt{135-35}} =\frac{2x}{\sqrt{270-45}}$

$\frac{\sqrt{64}}{\sqrt{100}} =\frac{2x}{\sqrt{225}}$

$\sqrt{64}=8\\\sqrt{100}=10\\\sqrt{225}=15$

$\frac{8}{10} =\frac{2x}{15}\\\\10*2x=8*15\\\\20x= 120\\\\x=120:20\\\\x=6$