(
)
⎛ ( 79 − 41) 792 + 79 ⋅ 41 + 412 ⎞ ⎛ 793 − 413 ⎞ + 79 ⋅ 41⎟ : (133,52 – 58,52) = ⎜ в) ⎜ + 79 ⋅ 41⎟ ⎜ 38 ⎟ ⎜⎜ ⎟⎟ 38 ⎝ ⎠ ⎝ ⎠
· (133,5–58,5)(133,5+ 58,5) = (79 + 41)2 : (75 · 192) = 1202 : 14400 = 1; ⎛ 693 + 293
г) (94,52 – 30,52) : ⎜ ⎜ ⎝
98
⎞ − 69 ⋅ 29 ⎟ = ⎟ ⎠
⎛ (69 + 29)(692 − 69 · 29 + 292 ) ⎞ 69 · 29 ⎟ = ⎟ 98 ⎝ ⎠
= (94,5 – 30,5)(94,5 + 30,5) ⎜ ⎜
= 64 · 125 : (69 – 29)2 = 8000 : 1600 = 5. № 636 а) a2 + ∗ + b2 = (a + b)2; б) b2 + 20ab + ∗ = (b + 10)2; в) ∗ – 56a + 49 = (4a – 7)2; г) ∗1 – 12c + ∗2 = (3c – 2)2;
(a + b)2 = a2 + 2ab + b2; ∗ = 2ab; (b + 10)2 = b2 + 20ab + 100; ∗ = 100; (4a – 7)2 = 16a2 – 56a + 49; ∗ = 16a; (3c – 2)2 = 9c2 – 12c + 4; ∗1 = 9c2, ∗2 = 4.
№ 637 а) b2 – 20b + ∗1 = (∗2 – 10)2; (∗2–10)2=∗22 – 2 · ∗2 · 10 + 100; ∗1=100, ∗2=b; б) ∗1 – 42pq+49q2 = (3p – ∗2)2; (3p–∗2)2=9p2–2 · ∗2 · 3p+∗22; ∗1=9p2, ∗2=7q; 1 1 в) 25a2 + ∗1 + b2 = (∗2 + b)2; 4 2 1 2 1 2 2 (∗2 + b) = ∗2 + ∗2b + b ; ∗2 = 5a, ∗1 = ∗2 · b = 5ab; 2 4 г) 0,01b2 + ∗1 + 100c2 = (0,1b + ∗2)2; (0,1b + ∗2)2 = 0,01b2 – 0,2b · ∗2 + ∗22; ∗2 = 10c, ∗1 = ∗2 · 0,2b = 10c · 0,2b = 2bc. № 638 а) ∗1 + 56ab + 49b2 = (4a + ∗2)2; (4a + ∗2)2 = 16a2 + 2 · ∗2 · 4a + ∗22; ∗1 = 16a2, ∗2 = 7b; б) 225x2 – ∗1 + 64y2 = (15x – ∗2)2; (15x – ∗2)2 = 225x2 – 2 · 15x · ∗2 + ∗22; ∗2 = 8y, ∗1 = 30x · ∗2 = 30x · 8y = 240xy; в) ∗1 + 96xy + 36y2 = (8x + ∗2)2; (8x + ∗2)2 = 64x2 + 16x · ∗2 + ∗22; ∗1 = 64x2, ∗2 = 6y; г) 100a2 + ∗1 + 49b2 = (10a + ∗2)2; (10a + ∗2)2 = 100a2 + 20a · ∗2 + ∗22; ∗2 = 7b, ∗1 = 140ab. № 639 а) m2 + 40m + ∗1 = (∗2 + 20)2; (∗2 + 20)2 = ∗22 + 2 · 20 · ∗2 + 400; ∗1 = 400, ∗2 = m; б) ∗1 – 70pq + ∗2 = (7p – ∗3)2; (7p – ∗3)2 = 49p2 – 2 · 7p · ∗3 + ∗32;
105