If a - b - c - 9 and ab - bc - ca - 23- then a2-b2-c2- none of these3512758

The correct option is B 35 a+b+c=9,ab+bc+ca=23 Squaring, (a+b+c)^2=(9)^2 a^2+b^2+c^2+2(ab+bc+ca)=81 ⇒ a^2+b^2+c^2+2×23=81 ⇒ a^2+b^2+c^2+46=81 ⇒ a^2+b^2+c^2=8 ...

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, then $a^{2} + b^{2} + c^{2}$ =

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

127

No worries! We‘ve got your back. Try BYJU‘S free classes today!

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
35

$a + b + c = 9, a b + b c + c a = 23 Squaring, (a + b + c)^{2} = (9)^{2} a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 81 \Rightarrow a^{2} + b^{2} + c^{2} + 2 \times 23 = 81 \Rightarrow a^{2} + b^{2} + c^{2} + 46 = 81 \Rightarrow a^{2} + b^{2} + c^{2} = 81 - 46 = 35$

Suggest Corrections

Similar questions

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. If

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

and

a b + b c + c a = 23

; find

a + b + c

Q. If a² + b² + c² + ab + bc + ca = 89 and (a + b) : (b + c) : (c + a) = 12 : 5 : 3, where a, b and c are real numbers, then (a² + b² + c² – ab – bc – ca) equals

यदि a² + b² + c² + ab + bc + ca = 89 तथा (a + b) : (b + c) : (c + a) = 12 : 5 : 3, जहाँ a, b व c वास्तविक संख्याएँ हैं, तब (a² + b² + c² – ab – bc – ca) बराबर है

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 = 9

and

a b + b c + c a = 26

, then the value of

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

Join BYJU'S Learning Program

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

The correct option is A 35 a+b+c=9,ab+bc+ca=23Squaring,(a+b+c)2=(9)2a2+b2+c2+2(ab+bc+ca)=81⇒ a2+b2+c2+2×23=81⇒ a2+b2+c2+46=81⇒ a2+b2+c2=81−46=35

If a + b + c = 9 and ab + bc + ca = 23, then $a^{2} + b^{2} + c^{2}$ =

The correct option is A
35

$a + b + c = 9, a b + b c + c a = 23 Squaring, (a + b + c)^{2} = (9)^{2} a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 81 \Rightarrow a^{2} + b^{2} + c^{2} + 2 \times 23 = 81 \Rightarrow a^{2} + b^{2} + c^{2} + 46 = 81 \Rightarrow a^{2} + b^{2} + c^{2} = 81 - 46 = 35$