find the fourth propotional a^2-5a+6,a^2+a-6,a^2-9
Answers
Answer:
Third proportional to (a
2
−5a+6),(a
2
+a−6)
= Third proportional to (a−2)(a−3),(a−2)(a+3)
Let the third proportional be p. Then:
(a−2)(a+3)
(a−2)(a−3)
=
p
(a−2)(a+3)
⇒p=
(a−2)(a−3)
[(a−2)(a+3)]
2
⇒p=(a−2)
a−3
(a+3)
2
(b) Find the Fourth proportional to
a
2
−5a+6,a
2
+a−6,a
2
−9
Let the fourth proportional be p. Then:
a
2
+a−6
a
2
−5a+6
=
p
a
2
−9
⇒
(a−2)(a+3)
(a−2)(a−3)
=
p
(a−3)(a+3)
⇒p=
(a−2)(a−3)
(a−2)(a+3)(a−3)(a+3)
⇒p=(a+3)
2
So fourth proportional is (a+3)
2
Step-by-step explanation:
(a)Third proportional to (a
2
−5a+6),(a
2
+a−6)
= Third proportional to (a−2)(a−3),(a−2)(a+3)
Let the third proportional be p. Then:
(a−2)(a+3)
(a−2)(a−3)
=
p
(a−2)(a+3)
⇒p=
(a−2)(a−3)
[(a−2)(a+3)]
2
⇒p=(a−2)
a−3
(a+3)
2
(b) Find the Fourth proportional to
a
2
−5a+6,a
2
+a−6,a
2
−9
Let the fourth proportional be p. Then:
a
2
+a−6
a
2
−5a+6
=
p
a
2
−9
⇒
(a−2)(a+3)
(a−2)(a−3)
=
p
(a−3)(a+3)
⇒p=
(a−2)(a−3)
(a−2)(a+3)(a−3)(a+3)
⇒p=(a+3)
2
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So fourth proportional is (a+3)
2