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Expansions (Including Substitution) — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSExpansions (Including Substitution)2 Marks
Question
If $a^2+ b^2 = 34$ and $ab = 12; $find $: 3(a + b)^2+ 5(a - b)^2$
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Answer

$a^2+b^2= 34,ab= 12$
$(a+b)^2=a^2+b^2+2ab$
$= 34 + 2 \times 12 = 34 + 24 = 58$
$(a-b)^2=a^2+b^2-2ab$
$= 34 - 2 \times 12 = 34- 24 = 10$
$3(a + b)^2+5(a-b)^2$
$= 3 \times 58 + 5 \times 10$
$= 174 + 50$
$= 224$

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