Răspuns:
Explicație pas cu pas:
a) (√4-√2)²=4-4√2+2=6-4√2
b) (2√3-√5)²=12-4√15+5=17-4√15
c)(√9-√8)=3√3-2√2
d)(√8+√8)=2·√4√2=4√2
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Bună,
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[tex]a) {( \sqrt{4} - \sqrt{2} )}^{2} = \\ (2 - \sqrt{2} ) ^{2} = \\ {2}^{2} - 2 \times 2 \times \sqrt{2} + ( \sqrt{2}) ^{2} = \\ 4 - 4 \sqrt{2} + 2 = \\ \blue{6 - 4 \sqrt{2} = 2(3 - 2 \sqrt{2} ) } \\ \\ b) {(2 \sqrt{3} - \sqrt{5} ) }^{2} = \\ (2 \sqrt{3}) ^{2} - 2 \times 2 \sqrt{3} \times \sqrt{5} + ( \sqrt{5} ) ^{2} = \\ 12 - 4 \sqrt{15} + 5 = \\ \red{17 - 4 \sqrt{15} } \\ [/tex]
[tex]c)( \sqrt{9} - \sqrt{8} ) = \\ 3 - \sqrt{ {2}^{2} \times 2} = \\ \green{3 - 2 \sqrt{2} } [/tex]
[tex]d)( \sqrt{8} + \sqrt{8} ) = \\ 2 \sqrt{2} + 2 \sqrt{2} = \\ \purple{4 \sqrt{2} } \\ \\ \\ \\ [/tex]
[tex]-•-•--•-•-•-•-•-•-•-• \\ {(a + b)}^{2} = {a}^{2} + 2ab + b ^{2} \\ (a - b) ^{2} = a ^{2} - 2ab + {b}^{2} [/tex]
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Sper că te-am ajutat.