Question

Q.
a = √5 - 2√3
b = 3√3 - 2√5
hitunglah nilai dari (a - b)² ​

Answer 1

Penjelasan dengan langkah-langkah:

[tex]\tt (a - b)^2\\\\= ((\sqrt{5}- 2\sqrt{3}) - (3\sqrt{3} -2\sqrt{5} ))^2\\\\= ((1+2)\sqrt{5} +(-2-3)\sqrt{3})^2\\\\=45-30\sqrt{15} +25(3)\\\\= 120-30\sqrt{15} \\\\= 3,8105[/tex]

Answer 2

Verified answer

Jawaban:

[tex] \huge { \blue {120 - 30 \sqrt{15} }} [/tex]

Penjelasan dengan langkah-langkah:

Sederhanakan:

=> [tex] (a - b)^{2} \\ (( \sqrt{5} - 2 \sqrt{3} ) - (3 \sqrt{3} - 2 \sqrt{5} ))^{2} \\ (\sqrt{5} - 2 \sqrt{3} - 3 \sqrt{3} + 2 \sqrt{5} )^{2} \\ \boxed{(3 \sqrt{5} - 5 \sqrt{3} )^{2}} [/tex].

Rumus: [tex] \boxed{(a - b)^{2} = {a}^{2} - 2ab + {b}^{2} } [/tex], dengan a = [tex] 3 \sqrt{5} [/tex] dan b = [tex] 5 \sqrt{3} [/tex].

Maka:

[tex] (a - b)^{2} = {a}^{2} - 2ab + {b}^{2} \\ (3 \sqrt{5} - 5 \sqrt{3} )^{2} = (3 \sqrt{5} )^{2} - 2(3 \sqrt{5} )(5 \sqrt{3} ) + {(5 \sqrt{3}) }^{2} [/tex]

[tex]( {3}^{2} \times { \sqrt{5} }^{2} ) - ((2 \times 3 \times 5) \sqrt{(5 \times 3)} ) + (5^{2} \times \sqrt{3} ^{2}) \\ (9 \times 5) - (30 \sqrt{15} ) + (25 \times 3) \\ 45 - 30 \sqrt{15} + 75 \\ \boxed{120 - 30 \sqrt{15} }[/tex]

Jadi, nilai dari (a-b)² adalah [tex] \blue {120 - 30 \sqrt{15} } [/tex].

[tex] \large {\boxed {\blue {\star \:Answered \: By: \: \bold {sulkifli2018} \star} } } [/tex]