Question

find the fourth propotional a^2-5a+6,a^2+a-6,a^2-9​

Answer 1

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

Answer 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