Question

If a^2+b^2=42 and ab=12 find 3(a+b)^2+5(a-b)^2

Answer 1

Given

a²+b²=42 i eq.

ab=12 ii eq.

To Find

3(a+b)²+5(a-b)²

Solution

a²+b²+2ab-2ab=42

(a+b)²-2ab=42

(a+b)²-24=42 [from eq. ii]

(a+b)²=66

similarly,

a²+b²-2ab+2ab=42

(a-b)²+2ab=42

(a-b)²+24=42 [from eq. ii]

(a-b)²=18

now,

=(3×66)+(5×18)

= 188+90

= 278

278 is ur answers

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