高中数学,这一题第二问怎么写?
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(1)(1+5+10)/32=1/2.
(2)1/32*(1-p)^2+[1/32*2(1-p)+5/32*(1-p)^2]+[1/32+5/32*2(1-p)+10/32*(1-p)^2]
+[5/32+10/32*2(1-p)+10/32*(1-p)^2]
=(1/32)[(1-p)^2+2(1-p)+5(1-p)^2+1+10(1-p)+10(1-p)^2+5+20(1-p)+10(1-p)^2]
=(1/32)[26(1-p)^2+32(1-p)]<1/2,
13(1-p)^2+16(1-p)-8<0,
(-8-2√42)/13<1-p<(-8+2√42)/13,0<=p<=1,
∴(21-2√42)/13<p<=1,(21-2√42)/13≈0.618
(2)1/32*(1-p)^2+[1/32*2(1-p)+5/32*(1-p)^2]+[1/32+5/32*2(1-p)+10/32*(1-p)^2]
+[5/32+10/32*2(1-p)+10/32*(1-p)^2]
=(1/32)[(1-p)^2+2(1-p)+5(1-p)^2+1+10(1-p)+10(1-p)^2+5+20(1-p)+10(1-p)^2]
=(1/32)[26(1-p)^2+32(1-p)]<1/2,
13(1-p)^2+16(1-p)-8<0,
(-8-2√42)/13<1-p<(-8+2√42)/13,0<=p<=1,
∴(21-2√42)/13<p<=1,(21-2√42)/13≈0.618
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