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daca a^2 -b^2 =40 si a-b=4 atunci a+b este egal cu...?
scris ca patratul unei sume x^2 +2√6x +6 devine...?
daca A=7+2x si B=2x-3 sa se calculeze A^2 + B^2
daca a^2 - b^2=21 si a+b=7. calculati :(a-b)+(a-b)^2 + (a-b)^3
daca x+ 1supra x =2 , culaculati x^2 + 1supra x^2

Răspuns :

Abc112
[tex] {a}^{2} - {b}^{2} = 40[/tex]

[tex]a - b = 4[/tex]

[tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex]

[tex](a - b)(a + b) = 40[/tex]

[tex]4(a + b) = 40 \: | \div 4[/tex]

[tex]a + b = 10[/tex]

[tex] {x}^{2} + 2 \sqrt{6} x + 6 = {(x + \sqrt{6} )}^{2} [/tex]

[tex]a = 7 + 2x[/tex]

[tex]b = 2x - 3[/tex]

[tex] {a}^{2} + {b}^{2} = {(7 + 2x)}^{2} + {(2x - 3)}^{2} [/tex]

[tex] = 49 + 28x + 4 {x}^{2} + 4 {x}^{2} - 12x + 9[/tex]

[tex] = 8 {x}^{2} + 16x + 58[/tex]

[tex] {a}^{2} - {b}^{2} = 21[/tex]

[tex]a + b = 7[/tex]

[tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex]

[tex](a - b) \times 7 = 21[/tex]

[tex]7(a - b) = 21 \: | \div 7[/tex]

[tex]a - b = 3[/tex]

[tex]a - b + {(a - b)}^{2} + {(a - b)}^{3} [/tex]

[tex]3 + {3}^{2} + {3}^{3} = 3 + 9 + 27 = 12 + 27 = 39[/tex]

[tex] x+\frac{ 1}{x} = 2\:|\times\:x[/tex]

[tex]{x}^{2} + 1 = 2x[/tex]

[tex]{x}^{2} - 2x +1= 0[/tex]

[tex]{x}^{2}-x-x+1=0[/tex]

[tex]x(x-1)-(x-1)=0[/tex]

[tex](x-1)(x-1)=0[/tex]

[tex]x-1=0=>x=1[/tex]

[tex] {x}^{2} +\frac{ 1 }{ {x}^{2} } = {1}^{2} + \frac{1}{ {1}^{2} } = 1+\frac{1}{1}=1+1=2[/tex]

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