01) Encontre o VALOR DE K sabendo que o resto da divisão de P (x) = x4 + kx² + kx – 7 por (x - 2) é 21.
02)- Determine o valor de a e b afim de que (x + a)² + ( b – x)² ≡ 2x² + 10x + 53
01)
p(2)=21
16+4k+2k-7=21
6k=21-9
k=12/6
k=2
02)
x²+2ax+a²+b²-2bx+x²=2x²+10x+53
2x²+(2a-2b)x+a²+b²=2x²+10x+53
2x²=2x²
2a-2b=10
2(a-b)=10
a-b=5
a=5-b
a²+b²=53
(5-b)²+b²=53
25-10b+b²+b²=53
2b²-10b-28=0
b²-5b-14=0
b=5+-raiz 25+56/2
b=5+-9/2
b'=5+9/2=7 a=5-b=5-7=-2 (-2,7)
b"=5-9/2=-2 a=5-b=5+2=7 (7,-2)
1)(2)^4+4k+2k-7=21
16+6k-7=21
6k=12
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Answers & Comments
Verified answer
01)
p(2)=21
16+4k+2k-7=21
6k=21-9
k=12/6
k=2
02)
x²+2ax+a²+b²-2bx+x²=2x²+10x+53
2x²+(2a-2b)x+a²+b²=2x²+10x+53
2x²=2x²
2a-2b=10
2(a-b)=10
a-b=5
a=5-b
a²+b²=53
(5-b)²+b²=53
25-10b+b²+b²=53
2b²-10b-28=0
b²-5b-14=0
b=5+-raiz 25+56/2
b=5+-9/2
b'=5+9/2=7 a=5-b=5-7=-2 (-2,7)
b"=5-9/2=-2 a=5-b=5+2=7 (7,-2)
1)(2)^4+4k+2k-7=21
16+6k-7=21
6k=21-9
6k=12
k=12/6
k=2