If a - b - c - 9 and ab - bc - ca - 23- find the value of a2 - b2 - c2

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) ⇒ (9)2 = a2 + b2 + c2 + 2 x 23 ⇒ 81= a2 + b2 + c2+ 46 ⇒ nbsp; a2 + b2 + c2 = 81 – 46 = 35 ∴ a^2+b^2+c^2=35 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Algebraic Identities

If a + b + c ...

Question

If a + b + c = 9 and ab + bc + ca = 23, find the value of a² + b² + c²

Open in App

Solution

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ (9)² = a² + b² + c²+ 2 x 23
⇒ 81= a² + b² + c²+ 46
⇒ a² + b² + c² = 81 – 46 = 35
$∴ a^{2} + b^{2} + c^{2} = 35$

Suggest Corrections

Similar questions

Q. If

a^{2} + b^{2} + c^{2} = 35

and

a b + b c + c a = 23

; find

a + b + c

Find $a^{2} + b^{2} + c^{2}; i f a + b + c = 9 a n d a b + b c + c a = 24$

Q. If a+b+c=0 what is the value of

\frac{a^{2} + b^{2} + a b}{b^{2} + c^{2} + b c} + \frac{c^{2} + c a + a^{2}}{b^{2} + c^{2} + b c}

Q. If a + b + c = 9 and ab + bc + ca = 23, then a² + b² + c² =

(a) 35

(b) 58

(c) 127

(d) none of these

Q. Question 30
if

a + b + c = 9

and

a b + b c + c a = 26

, find

a^{2} + b^{2} + c^{2}

Join BYJU'S Learning Program

If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) ⇒ (9)2 = a2 + b2 + c2 + 2 x 23 ⇒ 81= a2 + b2 + c2+ 46 ⇒ a2 + b2 + c2 = 81 – 46 = 35 ∴ a2+b2+c2=35

If a + b + c = 9 and ab + bc + ca = 23, find the value of a² + b² + c²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ (9)² = a² + b² + c²+ 2 x 23
⇒ 81= a² + b² + c²+ 46
⇒ a² + b² + c² = 81 – 46 = 35
$∴ a^{2} + b^{2} + c^{2} = 35$