A = $\sqrt{3 + 2\sqrt{2}}$ `-` $\sqrt{3 - 2\sqrt{2}}$ B = $\sqrt{9 + 4\sqrt{5}}$ `-` $\sqrt{9 - 4\sqrt{5}}$
2 câu trả lời
Đáp án :
`A = 2 ; B = 4 .`
Giải thích các bước giải :
`A = \sqrt{3 + 2\sqrt{2}} - \sqrt{3 - 2\sqrt{2}}`
`A = \sqrt{2} + 1 - (\sqrt{2} - 1)`
`A = \sqrt{2} + 1 - \sqrt{2} + 1`
`A = 1 + 1`
`A = 2 .`
`text{________________________________}`
`B = \sqrt{9 + 4\sqrt{5}} - \sqrt{9 - 4\sqrt{5}}`
`B = \sqrt{5} + 2 - (sqrt{5} - 2)`
`B = \sqrt{5} + 2 - \sqrt{5} + 2`
`B = 2 + 2`
`B = 4 .`
`text{#Muối}`
` A = √3 + 2√2 - √3 - 2 √2`
Ta có :
`3−2√2=(√2)^2−2.√2.1+1^2=(√2−1)^2`
`3+2√2=(√2 )^2 + 2 .√2.1+1^2 = (√2+1 )^2`
`=> A=√3 − 2√ 2− √3 + 2 √2`
`A=√(√2−1)^2 −√(√2+1)^2`
`A=∣√2−1∣−∣√2+ 1∣`
`A=(√2−1)−(√2+1 ) ( Do √2−1>0; √2+1>0)`
`A=√2−1−√2−1=−2`
`Vậy A = -2`
_______________________________________
`B = √9+4√5 -√9-4√5`
` B = √5 + √2 - ( √5 - 2 )`
` B = √5 + 2 - √5 + 2`
` B = 4`
$#phamnien$