P आकृतमध्ये रेषा रेषा = 80° तरRHD RP ms a रेखा Dहित्यचिदिका आहे. lli)
Answers
Answer:
Given α,β and γ are the roots of x
3
−3x
2
+3x+7=0
x=−1 is the root of equation x
3
−3x
2
+3x+7=0
x+1 should divide x
3
−3x
2
+3x+7=0
x+1)x
3
−3x
2
+3x+7(x
2
−4x+7
x
3
+x
2
_______________
−4x
2
+3x+7
−4x
2
−4x
______________
7x+7
7x+7
___________
x
___________
(x
3
−3x
2
+3x+7)=0
⇒(x+1)(x
2
−4x+7)=0
⇒x+1=0;x
2
−4x+7=0
x=−1 x=
2
4±
16−28
x=
2
4±
12
i
x=2±
3
i
Let α=−1,β=2+
3
i, r=2−
3
i
β−1
α−1
+
γ−1
β−1
+
α−1
γ−1
=
1+
3
i
−2
+
1−
3
i
1+
3
i
−
+2
1−
3
i
=
4
(−2)(1−
3
i)
+
4
(1+
3
ii)
2
+
(+2)
(1+
3
i)
Multiplying & dividing first term by (1−
3
i) & second term by (1+
3
i)
=
4
−2+2
3
i+1−3+2
3
i−2+2
3
i
=
4
−6+6
3
i
=
2
−3
+
2
3
3
i=3×(
2
−1
+
2
3
I)=3ω
2
∴
β−1
α−1
+
α−1
β−1
+
α−1
γ−1
=3ω
2
.
Answer:
One of the most widely used commercial hierarchical databases is IMS. Another example of the use of hierarchical databases is Windows Registry in the Microsoft Windows operating systems.