# Selina Solutions Class 9 Mathematics Solutions for Exercise 4(D) in Chapter 4 - Chapter 4- Expansions

Question 5 Exercise 4(D)

\text { If } a^{2}+b^{2}=34 \text { and } a b=12 ; \text { find: }

(i)(a+b)^{2}+5(a-b)^{2}

(ii)(a+b)^{2}+5(a-b)^{2}

a² + b² = 34, ab= 12

(a + b)² = a² + b² + 2ab

= 34 + 2 x 12 = 34 + 24 = 58

(a - b)² = a² + b² - 2ab

= 34 - 2 x 12 = 34- 24 = 10

(i) 3(a + b)² + 5(a - b)²

= 3 x 58 + 5 x 10 = 174 + 50

= 224

(ii) 7(a - b)² - 2(a + b)²

= 7 x 10 - 2 x 58 = 70 - 116 = -46

Video transcript
"hello students welcome to leader learning question answer video solution today's problem is if a square plus b square is 34 and a b is 12 we need to find the value of this problem my name is pulsha uh by the way so let's get started so we needs to find the value of 3 a plus b whole square plus 5 a minus b whole square so guys get ready with your identities because we're going to use lots of identities so let's get started a plus b square can be written as a square plus b square plus twice of a b similarly a minus b can be written as a square plus b square minus off to a b now let's start substituting the values because you should know that a square plus b square is 34 and a b is 12. so a square plus b square is 34. plus a b is 12 bracket close similarly a square plus b square is 34 minus of 2 times 12. now these are the values now start simplifying guys now 34 minus 12 times 2 is 24. similarly 34 minus 24 now that's the simplified version of the problem now let's keep on solving it now 34 plus 24 will be 58 and 34 minus 24 would be 10. 58 times 3 would be 174 and 5 times 10 is 50. so 174 plus 50 will give us 224 as an answer thank you so much for watching the video kids please keep it in mind that we needs to make sure that we remember our identities without identities it would be a little little typical job but i hope you can do it thank you so much for watching the video kids have a wonderful day for more fun videos subscribe to leader god bless you"
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