Question

If ab: bc: ac = 3: 4: 5, then find a^2: b^2: c^2.

Answer 1

Step-by-step explanation:

A-b = 3……..(1)

b-c= 5 ………….(2)

On adding eq 1& 2

a-c= 8 …………….(3)

From eq 1

a-b= 3

a= 3+b……………(4)

From eq 2

b-c = 5

b = 5+c…………….(5)

From eq 3

a-c = 8

c= a-8……………(6)

a²+b²+c²-ab-bc-ca (given)

= a²-ab +b²-bc+c²-ca

=a(a-b) + b(b-c)+ c (c-a)

=a(3) + b (5) + c (-8)

[ From eq 1, 2,3]

=3a+5b -8c

3a + 5(5+c) -8(a-8)

[ From eq 5,6]

=3a + 5 (5+a-8) -8a+64. ( c=a-8)

=3a + 25 +5a -40-8a+64

=3a+5a-8a+25-40+64

=8a -8a-15+64

a²+b²+c²-ab-bc-ca = 49

Answer 2

$ab : bc = 3 : 4 \\</p><p>\frac{ab}{bc} = \frac{a}{c} = \frac{3}{4}\\</p><p>or,\:(\frac{a}{c})^{2} = (\frac{3}{4})^{2}\\</p><p>or,\:{a}^{2} : {c}^{2} = {3}^{2}:{4}^{2} = 9:16 = 1:\frac{16}{9}</p><p>\\</p><p>Similarly,\\</p><p>bc:ac = 4:5\\</p><p>or, \:b:a=4:5\\</p><p>or, \:a:b=5:4\\</p><p>or, \:{a}^{2}:{b}^{2}=25:16=1:\frac{16}{25}\\ \\</p><p></p><p>So, \:\: {a}^{2}:{b}^{2}:{c}^{2} = 1:\frac{16}{25}:\frac{16}{9}\\</p><p><strong>Or</strong><strong>,</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>\</strong><strong>:</strong><strong>{a}^{2}:{b}^{2}:{c}^{2}=225:144:400</strong></p><p>$