CMR: 1,(a+b+c) ²=3(a²+b²+c²) 2. (a+b+c)²=3(ab+bc+ca) ❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤ 20/07/2021 Bởi Allison CMR: 1,(a+b+c) ²=3(a²+b²+c²) 2. (a+b+c)²=3(ab+bc+ca) ❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
Đáp án: 1. Ta có : `(a + b + c)^2 = 3(a^2 + b^2 + c^2)` `<=> 3(a^2 + b^2 + c^2) – (a + b + c)^2 = 0` `<=> 3a^2 + 3b^2 + 3c^2 – a^2 – b^2 – c^2 – 2ab – 2bc – 2ca = 0` `<=> 2a^2 + 2b^2 + 2c^2 – 2ab – 2bc – 2ca = 0` `<=> (a^2 – 2ab + b^2) + (b^2 – 2bc + c^2) + (c^2 – 2ca + a^2) = 0` `<=> (a – b)^2 + (b – c)^2 + (c – a)^2 = 0` `<=> a – b = b – c = c – a = 0` `<=> a = b = c` `2. Ta có : `(a + b + c)^2 = 3(ab + bc + ca)` `<=> (a + b + c)^2 – 3(ab + bc + ca) = 0` `<=> a^2 + b^2 + c^2 + 2ab + 2bc + 2ca – 3ab – 3bc – 3ca = 0` `<=> a^2 + b^2 + c^2 – ab – bc – ca = 0` `<=> 2a^2 + 2b^2 + 2c^2 – 2ab – 2bc – 2ca = 0` `<=> (a^2 – 2ab + b^2) + (b^2 – 2bc + c^2) + (c^2 – 2ca + a^2) = 0` `<=> (a – b)^2 + (b – c)^2 + (c – a)^2 = 0` `<=> a – b = b – c = c – a = 0` `<=> a = b = c` Giải thích các bước giải: Bình luận
Đáp án:
1. Ta có :
`(a + b + c)^2 = 3(a^2 + b^2 + c^2)`
`<=> 3(a^2 + b^2 + c^2) – (a + b + c)^2 = 0`
`<=> 3a^2 + 3b^2 + 3c^2 – a^2 – b^2 – c^2 – 2ab – 2bc – 2ca = 0`
`<=> 2a^2 + 2b^2 + 2c^2 – 2ab – 2bc – 2ca = 0`
`<=> (a^2 – 2ab + b^2) + (b^2 – 2bc + c^2) + (c^2 – 2ca + a^2) = 0`
`<=> (a – b)^2 + (b – c)^2 + (c – a)^2 = 0`
`<=> a – b = b – c = c – a = 0`
`<=> a = b = c`
`2. Ta có :
`(a + b + c)^2 = 3(ab + bc + ca)`
`<=> (a + b + c)^2 – 3(ab + bc + ca) = 0`
`<=> a^2 + b^2 + c^2 + 2ab + 2bc + 2ca – 3ab – 3bc – 3ca = 0`
`<=> a^2 + b^2 + c^2 – ab – bc – ca = 0`
`<=> 2a^2 + 2b^2 + 2c^2 – 2ab – 2bc – 2ca = 0`
`<=> (a^2 – 2ab + b^2) + (b^2 – 2bc + c^2) + (c^2 – 2ca + a^2) = 0`
`<=> (a – b)^2 + (b – c)^2 + (c – a)^2 = 0`
`<=> a – b = b – c = c – a = 0`
`<=> a = b = c`
Giải thích các bước giải: