Докажите тождество:
а)1/2 (m+n)²+1/2(m-n)²=m²+n²;
б)(1/2(m+n))²-(1/2(m-n))²=mn;
в)(7b-5c)²(b+2c)-b((7b+2c)²-119c²)=50c³;
Помогите пожалуйста
а)1/2 (m+n)²+1/2(m-n)²=m²+n²;
б)(1/2(m+n))²-(1/2(m-n))²=mn;
в)(7b-5c)²(b+2c)-b((7b+2c)²-119c²)=50c³;
Помогите пожалуйста
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Verified answer
A) 1/2 (m+n)² + 1/2 (m-n)² = m² + n²1/2 (m+n)² + 1/2 (m-n)² = 1/2 (m² + 2mn + n²) + 1/2 (m² - 2mn + n²) =
= 1/2 (2m² + 2 n²) = 1/2 * 2(m²+n²) = m²+n²
б) (1/2 (m+n))² - (1/2(m-n))² = mn
(1/2 (m+n))² - (1/2(m-n))² = (1/2)²(m+n)² - (1/2)²(m-n)² =
= 1/4 (m²+2mn+n² - m²+2mn - n²) = 1/4 * 4mn = mn
в) (7b-5c)²(b+2c) - b((7b+2c)² -119c²) = 50c³
(7b-5c)²(b+2c) - b((7b+2c)² -119c²) =
= (49b²-70bc+25c²)(b+2c) - b(49b²+28bc-119c²+4c²) =
= 49b³-70b²c+25bc²+98b²c-140bc²+50c³-49b³-28b²c+115bc² =
= 49b³-49b³+28b²c-28b²c-115bc²+115bc²+50c³ = 50c³