N²+m²+12²+3≥2(n+m+12)
n²+m²+12²+(1+1+1)≥2n+2m+2*12
n²-2n+1+m²-2m+1+12²-2*12+1≥0
(n-1)²+(m-1)²+(12-1)²≥0
доказано
А) 0,01234<0,0(12)
Б) -23,5>-23,(5)
В) 3/7=0,4285190...
Г) 4⅞>4,8(75)
√8а*√7х=√4*2а*√7х=2√2а*√7х
Х²=y
y²-6y+5-0
D= (-6 )² - 4×1×5 = 16
у 1 = 6-√16 ÷ 2 = 6 - 4 ÷ 2 = 1
у2 = 6 +√ 16 ÷2 = 6+4 ÷ 2 = 5
х² = 1 х² = 5
√х² = √1 √х²= √ 5
х = 1 х= √5
<span>Если формулу разности квадратов <span> <span>(a</span> – <span><span>b)</span><span>(a</span></span> + <span>b)</span> = <span>a 2</span> – <span>b 2</span> </span>
записать справа налево, то получится тождество
<span> <span>a 2</span> – <span>b 2</span> = <span>(a</span> – <span>b)</span> <span>(a</span> + <span>b)</span> </span>,
которое позволяет разложить разность квадратов на множители.
Оно читается так:
| <span> разность квадратов двух выражений равна произведению </span>
| <span> разности этих выражений и их суммы. </span>
<span> Примеры:
1) </span><span> 16<span>x 6</span> – <span>9<span>y 4</span></span> = <span><span>(<span>4<span>x 3</span></span>)</span> 2</span> – <span><span>(<span>3<span>y 2</span></span>)</span> 2</span> = <span>(<span>4<span>x 3</span></span></span> – <span><span>3<span>y 2</span></span>)</span> <span>(<span>4<span>x 3</span></span></span> + <span><span>3<span>y 2</span></span>)</span> ; </span>
<span> 2) </span><span> <span><span>1 <span>916</span></span><span>a 4</span></span> – <span><span>1 <span>79</span></span><span>b 6</span></span> = <span><span>2516</span><span>a 4</span></span> – <span><span>169</span><span>b 6</span></span> = <span><span>(<span> <span>54</span><span>a 2</span></span>)</span> 2</span> – <span><span>(<span> <span>43</span><span>b 3</span></span>)</span> 2</span> =
= <span>(<span> <span>54</span><span>a 2</span></span></span> – <span><span><span>43</span><span>b 3</span></span>)</span> <span>(<span> <span>54</span><span>a 2</span></span></span> + <span><span><span>43</span><span>b 3</span></span>)</span> ; </span>
<span> 3) </span><span> <span>975 2</span> – <span>25 2</span> = <span>(975</span> – <span>25)</span> <span>(975</span> + <span>25)</span> = 950 • 1000 = 950 000 ; </span>
<span> 4) </span><span> <span><span><span>4<span>x 4</span></span>−<span>9<span>y 4</span></span></span><span><span>2<span>x 2</span></span>−<span>3<span>y 2</span></span></span></span> = <span><span><span>(<span><span>2<span>x 2</span></span>−<span>3<span>y 2</span></span></span>)</span><span>(<span><span>2<span>x 2</span></span>+<span>3<span>y 2</span></span></span>)</span></span><span><span>2<span>x 2</span></span>−<span>3<span>y 2</span></span></span></span> = <span><span>2<span>x 2</span></span>+<span>3<span>y 2</span></span></span> .
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